Chapter 8.2, Problem 15E

Let x denote the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean value and standard deviation of x are μ = 2 minutes and σ ＝ 0.8 minutes, respectively.

1. a. If x̄ is the sample mean time for a random sample of n = 9 students, where is the sampling distribution of x̄ centered, and how much does it spread out around the center (as described by its standard deviation)?
2. b. Repeat Part (a) for a sample of size of n = 20 and again for a sample of size n = 100. How do the centers and variability of the three x̄ distributions compare to one another?
3. c. Which of the sample sizes in Part (b) would be most likely to result in an x̄ value close to μ, and why?