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

**Find the probability that the average review time is more than an hour:**

The amount of time an internal revenue service examiner is supposed to spend reviewing a randomly selected return is 55.1 minutes with a standard deviation of 17.6 minutes*. *That is, mean *μ* = 55.1 minutes and the population standard deviation is σ = $17.6 minutes. * *Random samples of 35 (*n*) reviews are drawn from the population. Let the random variable *X *denotes the amount of time an internal revenue service examiner is supposed to spend reviewing a randomly selected return. By central limit theorem for mean, the mean time of the sample follows a normal distribution with mean *μ* = 55.1 and standard deviation 17.6/sqrt (35) = 2.97. Thus, the probability that the average review time is more than an hour (60 minutes) is calculated as follows:

Step 3

Thus, the probability that the average review...

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