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
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
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