Question

Asked Oct 31, 2019

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Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population values.

2 | 3 | 2 | 3 | 3 | 4 | 2 | 4 | 3 | 2 | 2 | 7 | 3 | 4 | 5 | 3 | 3 | 3 | 3 | 5 |

a) If you were able to list all possible samples of size five from this population of 20, how would the sample means be distributed?

b) What would be the mean of the sample means? (Round your answer to 2 decimal places.)

c) What would be the standard deviation of the sample means? (Round your answer to 2 decimal places.)

Step 1

**Solution:**

**a.The distribution of sample means is identified below:**

**Central limit theorem:**

If the sample is selected from the population with finite mean and standard deviation, then the distribution of sample means follows normal distribution as sample size increases with regardless of population distribution.

According to central limit theorem sample means would tend to be **normally distributed.**

Step 2

**b.The mean of the sample means is obtained below:**

The mean of the sample mean is equal to the population mean.

The mean of the sample means ...

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