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, µ.

(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.

(f ) Repeat parts (b)–(e) using samples of size n = 3. Comment on the effect of increasing the sample size.