# Standard deviation, confidence interval

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1. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n=100 will be ______

a confidence interval for a population mean based on a sample of n=50

a) wider than

b) Narrower than

c) equal to

Explain answer:

2). If the box weights have a population mean =90lbs and a standard deviation of 24 lbs, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will "exceed" 94lbs is:

a) 34.13%

b) 84.13%

c) 15.87%

d) 56.36%

e) 16.87%

3. The width of a confidence interval will be:

a) Narrower for 99% confidence than 95% confidence

b) Wider for a sample size of 100 than for a sample size of 50

c) Marrower for 90% confidence than 95% confidence

d) Wider when the sample standard deviation (s) is small than when "s" is large

e) none of the above

4. If the box weights have a population mean of 90lbs and a standard deviation of 24lbs, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be "less" than 84 lbs is?

a) 16.87%

b) 93.32%

c) 43.32%

d) 6.678%

e) 84.13%

Explain answer:

5. The mean life of pair of shoes is 40 months with a standard devaition of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes "out of one million" will need replacement before 36 months?

a) 500,000

b) 808,500

c) 191,500

d) 308,500

Explain each answer:

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##### Solution Summary

1. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n=100 will be ______

a confidence interval for a population mean based on a sample of n=50

a) wider than

b) Narrower than

c) equal to

Explain answer:

2). If the box weights have a population mean =90lbs and a standard deviation of 24 lbs, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will "exceed" 94lbs is:

a) 34.13%

b) 84.13%

c) 15.87%

d) 56.36%

e) 16.87%

3. The width of a confidence interval will be:

a) Narrower for 99% confidence than 95% confidence

b) Wider for a sample size of 100 than for a sample size of 50

c) Marrower for 90% confidence than 95% confidence

d) Wider when the sample standard deviation (s) is small than when "s" is large

e) none of the above

4. If the box weights have a population mean of 90lbs and a standard deviation of 24lbs, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be "less" than 84 lbs is?

a) 16.87%

b) 93.32%

c) 43.32%

d) 6.678%

e) 84.13%

Explain answer:

5. The mean life of pair of shoes is 40 months with a standard devaition of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes "out of one million" will need replacement before 36 months?

a) 500,000

b) 808,500

c) 191,500

d) 308,500

Explain each answer:

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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