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Serga [27]
3 years ago
14

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 ~ _____(_____,_____)
Business
1 answer:
Inga [223]3 years ago
4 0

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

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