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 (). 61 45 25 61 56 (a) Compute the population mean, u. (b) Compute the mean for all C2 = 10 samples with size n=2. y Sample Sample Mean Sample Sample Mean 61.61 61,56 61.45 61.25 61,56 45,56 61,25 45,25 61,45 56,25 (c) Construct a sampling distribution for the mean by listing the sample means and their corresponding probabilities Give all the unique sample means in ascending order. (Type N if there is no solution) Sample Mean Probability Sample Mean Probability 6 F 1 7 2 3 JOOD . th Enter your answer in each of the answer boxes.

Answer 1

a. The population mean is

$\mu = 49.6$

b.

Sample	Sample Mean
61,61	61
61,45	53
61,56	58.5
61,25	43
61,45	53
61,56	58.5
61,25	43
45,56	50.5
45,25	35
56,25	40.5

c.

	Sample Mean	Probability
1	35	0.1
2	40.5	0.1
3	43	0.2
4	50.5	0.1
5	53	0.2
6	58.5	0.2
7	61	0.1
8	N	N
9	N	N
10	N	N

d. The mean od the sampling distribution is

49.6 years

e. Probability that sample mean is within 4 years of the population mean age

= P(Sample mean is between [45.6,53.6])

= 0.1 + 0.2

= 0.3

The probability is 0.3