Question

2. 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. 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.

Answer 1

The shape is going to be bell-shaped(normally distributed), with mean of 157 and standard deviation of
`(\sigma)/(√(n)) = (12)/(√(15)) = 3.1`

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, a large sample size can be approximated to a normal distribution with mean
`\mu` and standard deviation
`(\sigma)/(√(n))`.

So, in this problem:

The shape is going to be bell-shaped(normally distributed), with mean of 157 and standard deviation of
`(\sigma)/(√(n)) = (12)/(√(15)) = 3.1`