Question

A certain population has a mean of 486 and a standard deviation of 25. 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.)

(c) What shape would you expect the distribution of all these sample means to have?

skewed rightapproximately normal     skewed leftuniform

Answer 1

Solution :

Given that ,

mean = = 486

standard deviation = = 25

n = 57

a) Mean = = = 486

b) Standard deviation = = / n = 25/ 57 = 3.31

c) approximately normal