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 s = 0.8 minute, respectively.
a. If x is the sample mean time for a random sample of n = 9 students, where is the x distribution centered, and how much does it spread out about the center (as described by its standard deviation)?
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 spreads of the three x distributions compare to one another? Which sample size would be most likely to result in an x value close to m, and why?