Question

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 ~ _____(_____,_____)

Answer 1

Answer:

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 $\mu$ and standard deviation $\sigma$, a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$.

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 $n = 16$

The mean of the sample is the same as the population mean, so $\mu = 4$.

The standard deviation of the sample is $s = \frac{\sigma}{\sqrt{n}} = \frac{1.2}{4} = 0.3$