Question

Step 1

**Central Limit Theorem ****for mean****:**

If a random sample of size *n *is taken from a population having mean and standard deviation then, as the sample size increases, the sample mean approaches the normal distribution with mean and standard deviation σ/ sqrt(*n*).

Step 2

**Finding the probability that the average number of hours worked is more than 20 hours:**

The students typically work an average of 18.1 hours per week*. *That is, *μ* = 18.1.

The population standard deviation is σ = 15.3.

A random sample of 700 (*n*) freshmen from the community college is selected.

Let the random variable *X *denote the number of hours worked per week. By central limit theorem for mean, the mean price of the sample follows a normal distribution with mean μ = 18.1 and standard deviation 15.3/sqrt (700) = 0.5783.Thus, the probability that the average number of hours worked per week is more than 20 hours is calculated as follows:

Step 3

Thus, the probability that the average number of hours work...

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