The average weekly unemployment benefit in Montana is $272. Suppose that the benefits are normally distributed with a standard deviation of $43. A random sample of 15 benefits is chosen in Montana. What is the probability that the mean for this sample is greater than the U.S. average, which is $299? Is the normal distribution appropriate here since the sample size is only 15? Explain.

For Exercises assume that the sample is taken from a large population and the correction factor can be ignored.