Let x denote the time (in minutes) that it takes a fifth-grade student to read a certain...

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 minute, respectively.

a. If is the sample mean time for a random sample of n = 9 students, where is the 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 distributions compare to one another? Which sample size would be most likely to result in an value close to μ, and why?