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Concept explainers
New Residences The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the
a. Less than 10
b. Greater than 10
c. Between 11 and 12
a.
![Check Mark](/static/check-mark.png)
To obtain: The probability that a random sample of 36 people is less than 10.
Answer to Problem 9E
The probability that a random sample of 36 people is less than 10 is 0.00009.
Explanation of Solution
Given info:
Average number of moves a person makes in his or her lifetime is
Calculations:
The random variable x represents number of moves of a person in his/her lifetime.
The notation
The formula for finding the z score using central limit theorem is,
Substitute 10 for
The probability that the mean of the selected sample will be less than 10 moves represents the area to the left of 3.75.
Software procedure:
Step-by-step procedure to obtain the probability using the MINITAB software:
- Choose Graph > Probability Distribution Plot choose View Probability> OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0.0 and Standard deviation as 1.0.
- Click the Shaded Area tab.
- Choose X value and Left Tail for the region of the curve to shade.
- Enter the X value as –3.75.
- Click OK.
- Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people is less than 10 is 0.00009.
- b.
![Check Mark](/static/check-mark.png)
To obtain: The probability that a random sample of 36 people is greater than 10.
Answer to Problem 9E
Probability will be 0.9999.
Explanation of Solution
Calculations:
The formula for finding the z score using central limit theorem is,
Substitute 10 for
The probability that a random sample of 36 people greater than 10 represents the area to the right of –3.75.
Software procedure:
Step-by-step procedure to obtain the probability using the MINITAB software:
- Choose Graph > Probability Distribution Plot choose View Probability> OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0.0 and Standard deviation as 1.0.
- Click the Shaded Area tab.
- Choose X value and Right Tail for the region of the curve to shade.
- Enter the X value as –3.75.
- Click OK.
- Output using the MINITAB software is given below:
- From MINITAB output, the probability that a random sample of 36 people greater than 10 is 0.9999.
- c.
![Check Mark](/static/check-mark.png)
The probability that a random sample of 36 people between 11 and 12.
Answer to Problem 9E
The probability that a random sample of 36 people is between 11 and 12 is 0.4699.
Explanation of Solution
Calculations:
The formula for finding the z score using central limit theorem is,
Substitute 11 and 12 for
The probability that a random sample of 36 people is between 11 and 12 represents area between the value
Software procedure:
Step-by-step procedure to obtain the probability using the MINITAB software:
- Choose Graph > Probability Distribution Plot choose View Probability> OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0.0 and Standard deviation as 1.0.
- Click the Shaded Area tab.
- Choose X value and Middle for the region of the curve to shade.
- Enter the X value 1 as –1.88 and X value 2 as 0.
- Click OK.
- Output using the MINITAB software is given below:
From MINITAB output, the probability that a random sample of 36 people is between 11 and 12 is 0.4699.
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Chapter 6 Solutions
Elementary Statistics: A Step By Step Approach
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