Question: A magazine reports that the average bowling score for league bowlers in the United States is 157 with a standard deviation of 12, and that the scores are approximately normally distributed.

1. State the shape, the mean, and the standard deviation of the mean x of 15 bowlers selected at random. Justify each statement by showing your work or identifying the theorem that tells you your answer is correct. (4 points)
2. What's the probability that a random sample of 15 bowlers would have an average score greater than 165? (5 points)
3. What's the probability a random sample of 150 bowlers will have an average score greater than 165? (5 points)

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