Question

A rowing team consists of four rowers who weigh 52, 56, 60, and 64 pounds. Find all possible random samples with replacement of size two and compute the sample mean for each one. Use them to find the probability distribution, the mean, and the standard deviation of the sample mean

Answer 1

We have given 52, 56, 60 and 64

Possible random sample with replacement of size 2 are: (52,56); (52,60); (52,64); (56,60); (56,64); (60,64)

Possible Sample	Sample mean (X)	(X - Xbar)	(X - Xbar)2
(52,56)	(52+56)/2 = 54	-4	16
(52,60)	(52+60)/2 = 56	-2	4
(52,64)	(52+64)/2 = 58	0	0
(56,60)	(56+60)/2 = 58	0	0
(56,64)	(56+64)/2 = 60	2	4
(60,64)	(60+64)/2 = 62	4	16
Total	58		40

Mean of sample mean = (54+56+58+58+60+62)/6 = 58

Standard deviation of sample mean (SD):