The amounts of time employees at a large corporation work each day are normally

Question

The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.7 hours and a standard deviation of 0.33 hour. Random samples of size 25 and 34

are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases?

If the sample size is n = 25, find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample means is. (Type an integer or a decimal.)

The standard deviation of the distribution of sample means is. (Round to two decimal places as needed.)

If the sample size is n = 34, find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample means is. (Type an integer or a decimal.)

The standard deviation of the distribution of sample means is.

(Type an integer or decimal rounded to the nearest hundredth as needed.)

What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases? Choose the correct answer below.

A. The mean stays the same, but the standard deviation decreases.

B. The mean stays the same, but the standard deviation increases.

C. The mean and the standard deviation both increase.

D. The mean and the standard deviation both decrease.

Explanation / Answer

for n=25

mean of the distribution of sample means=7.7

standard deviation of the distribution of sample means =0.33/(25)1/2 =0.07

for n=34

mean of the distribution of sample means=7.7

standard deviation of the distribution of sample means=0.33/(34)1/2 =0.06

option A is correct

A. The mean stays the same, but the standard deviation decreases.

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