Question

The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions (a) through (e). 52 52 51 59 41 (a) Compute the population mean, (b) Compute the mean for all C2 = 10 samples with size n = 2. Sample Sample Mean 52,59 52,52 52,41 52,51 59,52 Sample Sample Mean 59,41 59,51 52.41 52,51 41,51

Answer 1

(a) $\mu$ = (52+52+51+59+41)/5 = 51.
(b) The table is given below.

1st element	2nd element	Sample	Sample Mean
52	59	52,59	55.5
52	52	52,52	52
52	41	52,41	46.5
52	51	52,51	51.5
59	52	59,52	55.5
59	41	59,41	50
59	51	59,51	55
52	41	52,41	46.5
52	51	52,51	51.5
41	51	41,51	46

(c) The table is given below.

S. No.	Sample Mean	Probability
1	46	0.1
2	46.5	0.2
3	50	0.1
4	51.5	0.2
5	52	0.1
6	55	0.1
7	55.5	0.2
8	N	N
9	N	N
10	N	N

(d) The mean of the sampling distribution is the mean of the "Sample Mean" column in part (b) = 51.

(e) Prob.(sample mean is between 47 and 55, both inclusive) = 5/10 = 0.50.