# that the amount of time an Internal Revenue Service examiner is supposed tospend reviewing a randomly selected return is 55.1 minutes, with a standard deviation ofabout 17.6 minutes. If a sample of 35 such reviews is selected, what is the probabilitythat the average review time is more than an hour?

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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