# Standard deviation, confidence interval

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:

Â© BrainMass Inc. brainmass.com May 24, 2023, 1:16 pm ad1c9bdddfhttps://brainmass.com/statistics/confidence-interval/standard-deviation-confidence-interval-15262

#### 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: