8.15 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 m 5 2 minutes and s 5 0.8 minutes, respectively.

a. If x is the sample mean time for a random sample of n 5 9 students, where is the x distribution centered, and how much does it spread out around the center (as described by its standard deviation)?

b. Repeat Part

(a) for a sample of size of n 5 20 and again for a sample of size n 5 100. How do the centers and spreads of the three x distributions compare to one another?

c. Which of the sample sizes in Part

(b) would be most likely to result in an x value close to m, and why?