A certain population has a mean of 491 and a standard deviat

A certain population has a mean of 491 and a standard deviation of 34. Many samples of size 57 are randomly selected and the means calculated.

(a) What value would you expect to find for the mean of all these sample means? (Give your answer correct to nearest whole number.)


(b) What value would you expect to find for the standard deviation of all these sample means? (Give your answer correct to two decimal places.)

Solution

here population mean is 491...sample size is 57 and population SD is 34

a) as the sample mean is unbiased for the population mean. so the mean of all these sample means would be approximately 491.

b) the standard deviation of all these sample means would be approximately 34/sqrt(57)=4.5034