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). (Assume that sampling is without replacement.)		41 41	42 42
38 38	48 48
44 44

a. Find the population mean age of the five winners.

mu

equals

=

nothing

years

b. For samples of size 3, construct a table of all possible samples and their sample means.

Age	x overbar x		Age	x overbar x
41 41, 42 42, 38 38	nothing	41 41, 48 48, 44 44	nothing
41 41, 42 42, 48 48	nothing	42 42, 38 38, 48 48	nothing
41 41, 42 42, 44 44	nothing	42 42, 38 38, 44 44	nothing
41 41, 38 38, 48 48	nothing	42 42, 48 48, 44 44	nothing
41 41, 38 38, 44 44	nothing	38 38, 48 48, 44 44	nothing

(Round to two decimal places as needed.)

c. Draw a dotplot for the sampling distribution of the sample mean for samples of

size 3.

size3. Choose the correct dotplot below.

A.

39

41

43

45

A dotplot, has a horizontal axis labeled from 39 to 46 in increments of 1. Vertical stacks of dots, centered on horizontal axis values, rise from the horizontal axis. The numbers of dots in the stacks are as follows, where the horizontal axis value is listed first and the number of dots is listed second: 40.3 comma 1 ; 41 comma 1 ; 41.3 comma 1 ; 42.3 comma 1 ; 42.7 comma 1 ; 43.3 comma 1 ; 43.7 comma 1 ; 44.3 comma 1 ; 44.7 comma 1. All values are approximate.

B.

39

41

43

45

A dotplot, has a horizontal axis labeled from 39 to 46 in increments of 1. Vertical stacks of dots, centered on horizontal axis values, rise from the horizontal axis. The numbers of dots in the stacks are as follows, where the horizontal axis value is listed first and the number of dots is listed second: 40 comma 1 ; 41 comma 1 ; 42 comma 1 ; 43 comma 1 ; 44 comma 1 ; 45 comma 1.

C.

39

41

43

45

A dotplot has a horizontal axis labeled from 39 to 46 in increments of 1. Vertical stacks of dots, centered on horizontal axis values, rise from the horizontal axis. The numbers of dots in the stacks are as follows, where the horizontal axis value is listed first and the number of dots is listed second: 40.3 comma 1 ; 41 comma 1 ; 41.3 comma 1 ; 42.3 comma 2 ; 42.7 comma 1 ; 43.3 comma 1 ; 43.7 comma 1 ; 44.3 comma 1 ; 44.7 comma 1. All values are approximate.

D.

39

41

43

45

A dotplot, has a horizontal axis labeled from 39 to 46 in increments of 1. Vertical stacks of dots, centered on horizontal axis values, rise from the horizontal axis. The numbers of dots in the stacks are as follows, where the horizontal axis value is listed first and the number of dots is listed second: 40 comma 1 ; 41 comma 2 ; 42 comma 2 ; 43 comma 2 ; 44 comma 2 ; 45 comma 1.

d. For a random sample of size 3, what is the chance that the sample mean will equal the population mean?

The probability is

nothing

.

(Type an integer or a decimal. Use the answers from part (a) and part (b) to find this answer.)

e. For a random sample of size 3, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be

2

2 years or less; that is, determine the probability that

x overbar

x will be within

2

2 years of

mu

.

The probability is

nothing

.

(Type an integer or a decimal. Use the answers from part (a) and part (b) to find this answer.)