Yoonie is a personnel manager in a large corporation. each month she must review 16 of the employees. from past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. let χ be the random variable representing the time it takes her to complete one review. assume χ is normally distributed. let 9 o be the random variable representing the mean time to complete the 16 reviews. assume that the 16 reviews represent a random set of reviews. 1. what is the mean, standard deviation, and sample size? 2. complete the distributions. a. x ~ b. 9 o ~

Sample size is 16

Mean 4

Standard deviation of the sample is 0.3.

Explanation

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , a large sample size can be approximated to a normal distribution with mean and standard deviation .

In this problem, we have that:

The population has a mean of four hours, with a standard deviation of 1.2 hours. The sample is the 16 of the employees.

So

The sample size is 16, so

The mean of the sample is the same as the population mean, so .

The standard deviation of the sample is

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