Sampling Distributions The following data represent the running lengths (in minutes) of the winners of the Academy Award for Best Picture for the years 2004-2009.
| 2004: Million Dollar Baby |
132 |
| 2005: Crash |
112 |
| 2006: The Departed |
151 |
| 2007: No Country for Old Men |
122 |
| 2008: Slumdog Millionaire |
120 |
| 2009: The Hurt Locker |
131 |
(a) Compute the population mean.
(b) List all possible samples with size n = 2. There should be 6C2 = 15 samples.
(c) Construct a sampling distribution for the mean by listing the sample means and their corresponding probabilities.
(d) Compute the mean of the sampling distribution.
(e) Compute the probability that the sample mean is within 5 minutes of the population mean running time.