Question

A sample of size n = 49 is selected from a population with mean E(X) = 58 and standard deviation SD(X) = 22. The expected value E(x) and standard deviation SD(x) of the sampling distribution of the sample mean x are:_______________

A) 58 and 0.67 respectively

B) 58 and 22, respectively    

C) 58 and 9.88 respectively

D) 58 and 3.14, respectively

E) 58 and 0.45 respectively

Answer 1

solution:

Solution :

Given that ,

mean = = E(X) = 58

standard deviation = SD(x)= = 22

n = 49

sampling distribution of the sample mean x is =E(X) = 58

sampling distribution of the standrad deviation   = SD(x)/ n = 22/ 49=3.14

correct option D) 58 and 3.14, respectively