Chapter 7.1, Problem 14E

Exercises 7.11–7.23 are intended solely to provide concrete illustrations of the sampling distribution of the sample mean. For that reason, the populations considered are unrealistically small. In each exercise, assume that sampling is without replacement.

7.14 NBA Champs. Repeat parts (b)–(e) of Exercise 7.11 for samples of size 4.

7.11 NBA Champs. The winner of the 2012–2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows.

Player	Position	Height (in.)
Chris Bosh (B)	Center	83
Dwyane Wade (W)	Guard	76
LeBron James (J)	Forward	80
Mario Chalmers (C)	Guard	74
Udonis Haslem (H)	Forward	80

1. a. Find the population mean height of the five players.
2. b. For samples of size 2, construct a table similar to Table 7.2 on page 310. Use the letter in parentheses after each player’s name to represent each player.
3. c. Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.
4. d. For a random sample of size 2, what is the chance that the sample mean will equal the population mean?

For a random sample of size 2, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be 1 inch or less; that is, determine the probability that $\bar{x}$ will be within 1 inch of μ. Interpret your result in terms of percentages.