Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

Question

Want to see the full answer?

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 7.8, Problem 98E

a.

To determine

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

b.

To determine

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)

c.

To determine

Explain the reason why the probabilities obtained in Part (b) are not equal.

d.

To determine

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

e.

To determine

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADO

Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?

A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

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 7.8, Problem 98E

a.

To determine

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

b.

To determine

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)

c.

To determine

Explain the reason why the probabilities obtained in Part (b) are not equal.

d.

To determine

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

e.

To determine

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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 7.8, Problem 98E

a.

To determine

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

b.

To determine

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)

c.

To determine

Explain the reason why the probabilities obtained in Part (b) are not equal.

d.

To determine

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

e.

To determine

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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 7.8, Problem 98E

a.

To determine

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

b.

To determine

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)

c.

To determine

Explain the reason why the probabilities obtained in Part (b) are not equal.

d.

To determine

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

e.

To determine

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 7.8, Problem 98E

a.

To determine

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

b.

To determine

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)

c.

To determine

Explain the reason why the probabilities obtained in Part (b) are not equal.

d.

To determine

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

e.

To determine

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Answer 6

Chapter 7.8, Problem 98E

a.

To determine

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

Answer 7

Chapter 7.8, Problem 98E

a.

To determine

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

Answer 8

b.

To determine

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)

Answer 9

b.

To determine

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)

Answer 10

c.

To determine

Explain the reason why the probabilities obtained in Part (b) are not equal.

Answer 11

c.

To determine

Explain the reason why the probabilities obtained in Part (b) are not equal.

Answer 12

d.

To determine

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

Answer 13

d.

To determine

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

Answer 14

e.

To determine

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Answer 15

e.

To determine

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 19

Ch. 7.1 - State whether each of the following random...Ch. 7.1 - Classify each of the following random variables as...Ch. 7.1 - Starting at a particular time, each car entering...Ch. 7.1 - A point is randomly selected from the interior of...Ch. 7.1 - A point is randomly selected on the surface of a...Ch. 7.1 - Prob. 6E Ch. 7.1 - A box contains four slips of paper marked 1, 2, 3,...Ch. 7.2 - Let x be the number of courses for which a...Ch. 7.2 - Let y denote the number of broken eggs in a...Ch. 7.2 - Suppose that fund-raisers at a university call...

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

Solution Summary: The author explains that the normal approximation to binomial distribution is applicable for the given situation.

Concept explainers

Videos

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)

Explain the reason why the probabilities obtained in Part (b) are not equal.

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Want to see the full answer?

Chapter 7 Solutions

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

Solution Summary: The author explains that the normal approximation to binomial distribution is applicable for the given situation.

Concept explainers

Videos

Check whether it is appropriate to use normal approximation to binomial distribution for the given situation.

Approximate the below probabilities: i. P(x=42) ii. P(x<42) iii. P(x≤42)

Explain the reason why the probabilities obtained in Part (b) are not equal.

Explain the reason to use binomial formula instead of using normal approximation to obtain the required probability.

Explain the reason why the authors of the study propose that someone who scores 42 or less on the MENT exam is faking the test.

Want to see the full answer?

Chapter 7 Solutions

Approximate the below probabilities:

i. P(x=42)

ii. P(x<42)

iii. P(x≤42)