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 = 5 minutes and a = 0.8 minutes, respectively. (a) If x is the sample mean time for a random sample of n = 9 students, where is the sampling distribution of x centered, and how much does it spread out around the center (as described by its standard deviation)? (Round your answers to three decimal places.) minutes minutes (b) Repeat part (a) for a sample of size of n = 20 and again for a sample of size n = 100. (Round your answers to three decimal places.) n 20 Hy = n = 100 minutes minutes minutes minutes How do the centers and variability of the three x distributions compare to one another? The centers of the distributions of the sample mean are ---Select--- ✓, and the standard deviations (and therefore spreads) of these distributions are ---Select--- (c) Which of the sample sizes in part (b) would be most likely to result in an x value close to μ, and why? A sample size of n = ---Select--- is most likely to result in a sample mean close to μ, since this is the sample size that results in the ---Select--- ✓of the distribution of x.