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 0.36 hour. Random samples of size 22 and 37 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?

1.If the sample size is n=22 find the mean and standard deviation of the distribution of sample means.

2.If the sample size is n=37 find the mean and standard deviation of the distribution of sample means.

3.What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample​ increases?

Answer 1

Here's the answer to the question. Please don't hesitate to give a thumbs up if you are satisfied with the answer.

1. If the sample size is 22 then the:

Mean = population mean = 7.7

Stdev = .36/sqrt(22)

2. If the sample size is 37 then :

Mean = population mean = 7.7

Stdev of sample = population dev/sqrt(n) = .36/sqrt(37)

3. As the size increases the mean remains same as the population mean. But the standard deviations of the sample decreases as the sample size increases. It becomes y/sqrt(n) times the population mean for a population deviation of y.