The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P ( 0 ≤ z ≤ 1.95 ) .

Question

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Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6, Problem 6.1.1RE

a.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0≤z ≤1.95) .

a.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Explanation of Solution

Given info:

The z values are 0 and 1.95.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 1

Therefore, P(0≤z ≤1.95)=0.4744.

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

b.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0≤z ≤0.37) .

b.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Explanation of Solution

Given info:

The z values are 0 and 0.37.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 2

Therefore, P(0≤z≤0.37)=0.1443 .

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

c.

To determine

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32≤z≤1.82) .

c.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Explanation of Solution

Given info:

The z values are 1.32 and 1.82.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 3

Therefore, P(1.32≤z≤1.82)=0.05904 .

Conclusion:

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

d.

To determine

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(−1.05≤z≤2.05) .

d.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Explanation of Solution

Given info:

The z values are –1.05 and 2.05.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 4

Therefore, P(−1.05≤z≤2.05)=0.8330 .

Conclusion:

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

e.

To determine

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(−0.03≤z≤0.53)

e.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Explanation of Solution

Given info:

The z values are -0.03 and 0.53.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 5

Therefore, P(−0.03≤z≤0.53)=0.2139 .

Conclusion:

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

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Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6, Problem 6.1.1RE

a.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0≤z ≤1.95) .

a.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Explanation of Solution

Given info:

The z values are 0 and 1.95.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 1

Therefore, P(0≤z ≤1.95)=0.4744.

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

b.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0≤z ≤0.37) .

b.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Explanation of Solution

Given info:

The z values are 0 and 0.37.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 2

Therefore, P(0≤z≤0.37)=0.1443 .

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

c.

To determine

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32≤z≤1.82) .

c.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Explanation of Solution

Given info:

The z values are 1.32 and 1.82.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 3

Therefore, P(1.32≤z≤1.82)=0.05904 .

Conclusion:

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

d.

To determine

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(−1.05≤z≤2.05) .

d.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Explanation of Solution

Given info:

The z values are –1.05 and 2.05.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 4

Therefore, P(−1.05≤z≤2.05)=0.8330 .

Conclusion:

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

e.

To determine

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(−0.03≤z≤0.53)

e.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Explanation of Solution

Given info:

The z values are -0.03 and 0.53.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 5

Therefore, P(−0.03≤z≤0.53)=0.2139 .

Conclusion:

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6, Problem 6.1.1RE

a.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0≤z ≤1.95) .

a.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Explanation of Solution

Given info:

The z values are 0 and 1.95.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 1

Therefore, P(0≤z ≤1.95)=0.4744.

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

b.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0≤z ≤0.37) .

b.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Explanation of Solution

Given info:

The z values are 0 and 0.37.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 2

Therefore, P(0≤z≤0.37)=0.1443 .

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

c.

To determine

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32≤z≤1.82) .

c.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Explanation of Solution

Given info:

The z values are 1.32 and 1.82.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 3

Therefore, P(1.32≤z≤1.82)=0.05904 .

Conclusion:

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

d.

To determine

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(−1.05≤z≤2.05) .

d.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Explanation of Solution

Given info:

The z values are –1.05 and 2.05.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 4

Therefore, P(−1.05≤z≤2.05)=0.8330 .

Conclusion:

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

e.

To determine

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(−0.03≤z≤0.53)

e.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Explanation of Solution

Given info:

The z values are -0.03 and 0.53.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 5

Therefore, P(−0.03≤z≤0.53)=0.2139 .

Conclusion:

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6, Problem 6.1.1RE

a.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0≤z ≤1.95) .

a.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Explanation of Solution

Given info:

The z values are 0 and 1.95.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 1

Therefore, P(0≤z ≤1.95)=0.4744.

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

b.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0≤z ≤0.37) .

b.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Explanation of Solution

Given info:

The z values are 0 and 0.37.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 2

Therefore, P(0≤z≤0.37)=0.1443 .

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

c.

To determine

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32≤z≤1.82) .

c.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Explanation of Solution

Given info:

The z values are 1.32 and 1.82.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 3

Therefore, P(1.32≤z≤1.82)=0.05904 .

Conclusion:

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

d.

To determine

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(−1.05≤z≤2.05) .

d.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Explanation of Solution

Given info:

The z values are –1.05 and 2.05.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 4

Therefore, P(−1.05≤z≤2.05)=0.8330 .

Conclusion:

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

e.

To determine

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(−0.03≤z≤0.53)

e.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Explanation of Solution

Given info:

The z values are -0.03 and 0.53.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 5

Therefore, P(−0.03≤z≤0.53)=0.2139 .

Conclusion:

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

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Answer 5

Chapter 6, Problem 6.1.1RE

a.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0≤z ≤1.95) .

a.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Explanation of Solution

Given info:

The z values are 0 and 1.95.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 1

Therefore, P(0≤z ≤1.95)=0.4744.

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

b.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0≤z ≤0.37) .

b.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Explanation of Solution

Given info:

The z values are 0 and 0.37.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 2

Therefore, P(0≤z≤0.37)=0.1443 .

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

c.

To determine

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32≤z≤1.82) .

c.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Explanation of Solution

Given info:

The z values are 1.32 and 1.82.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 3

Therefore, P(1.32≤z≤1.82)=0.05904 .

Conclusion:

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

d.

To determine

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(−1.05≤z≤2.05) .

d.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Explanation of Solution

Given info:

The z values are –1.05 and 2.05.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 4

Therefore, P(−1.05≤z≤2.05)=0.8330 .

Conclusion:

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

e.

To determine

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(−0.03≤z≤0.53)

e.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Explanation of Solution

Given info:

The z values are -0.03 and 0.53.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 5

Therefore, P(−0.03≤z≤0.53)=0.2139 .

Conclusion:

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Answer 6

Chapter 6, Problem 6.1.1RE

a.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0≤z ≤1.95) .

a.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Explanation of Solution

Given info:

The z values are 0 and 1.95.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 1

Therefore, P(0≤z ≤1.95)=0.4744.

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Answer 7

Chapter 6, Problem 6.1.1RE

a.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0≤z ≤1.95) .

Answer 8

a.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given info:

The z values are 0 and 1.95.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 1

Therefore, P(0≤z ≤1.95)=0.4744.

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Answer 13

b.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0≤z ≤0.37) .

b.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Explanation of Solution

Given info:

The z values are 0 and 0.37.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 2

Therefore, P(0≤z≤0.37)=0.1443 .

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Answer 14

b.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0≤z ≤0.37) .

Answer 15

b.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given info:

The z values are 0 and 0.37.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 2

Therefore, P(0≤z≤0.37)=0.1443 .

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Answer 20

c.

To determine

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32≤z≤1.82) .

c.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Explanation of Solution

Given info:

The z values are 1.32 and 1.82.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 3

Therefore, P(1.32≤z≤1.82)=0.05904 .

Conclusion:

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Answer 21

c.

To determine

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32≤z≤1.82) .

Answer 22

c.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given info:

The z values are 1.32 and 1.82.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 3

Therefore, P(1.32≤z≤1.82)=0.05904 .

Conclusion:

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Answer 27

d.

To determine

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(−1.05≤z≤2.05) .

d.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Explanation of Solution

Given info:

The z values are –1.05 and 2.05.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 4

Therefore, P(−1.05≤z≤2.05)=0.8330 .

Conclusion:

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Answer 28

d.

To determine

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(−1.05≤z≤2.05) .

Answer 29

d.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given info:

The z values are –1.05 and 2.05.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 4

Therefore, P(−1.05≤z≤2.05)=0.8330 .

Conclusion:

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Answer 34

e.

To determine

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(−0.03≤z≤0.53)

e.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Explanation of Solution

Given info:

The z values are -0.03 and 0.53.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 5

Therefore, P(−0.03≤z≤0.53)=0.2139 .

Conclusion:

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Answer 35

e.

To determine

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(−0.03≤z≤0.53)

Answer 36

e.

Expert Solution

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Answer 37

e.

Expert Solution

Answer 38

e.

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given info:

The z values are -0.03 and 0.53.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:

Select Graph > Probability Distribution Plot > View Probability >OK.
From Distribution, choose ‘Normal’ distribution.
Enter the Mean as 0.0 and Standard deviation as 1.0.
Choose the tab for Shaded Area, then X Value.
Click the picture for Middle.
Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
Click OK.

Output using the MINITAB software is given below:

Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St, Chapter 6, Problem 6.1.1RE , additional homework tip 5

Therefore, P(−0.03≤z≤0.53)=0.2139 .

Conclusion:

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Answer 41

Ch. 6.1 - Many times in statistics it is necessary to see if...Ch. 6.1 - What are the characteristics of an normal...Ch. 6.1 - Why is the standard normal distribution important...Ch. 6.1 - What is the total area under the standard normal...Ch. 6.1 - What percentage of the area falls below the mean?...Ch. 6.1 - About what percentage of the area under the normal...Ch. 6.1 - What are two other names for a normal...Ch. 6.1 - Prob. 7E Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 9E

The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P ( 0 ≤ z ≤ 1.95 ) .

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0≤z ≤1.95) .

Answer to Problem 6.1.1RE

Explanation of Solution

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0≤z ≤0.37) .

Answer to Problem 6.1.1RE

Explanation of Solution

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32≤z≤1.82) .

Answer to Problem 6.1.1RE

Explanation of Solution

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(−1.05≤z≤2.05) .

Answer to Problem 6.1.1RE

Explanation of Solution

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(−0.03≤z≤0.53)

Answer to Problem 6.1.1RE

Explanation of Solution

Want to see more full solutions like this?

Chapter 6 Solutions