Question

A manufacturer of all-in-one printers is concerned that the warranty costs for a particular printer model exceed the amount expected by the company. Based on a review of completed warranty claims, the distribution of the warranty cost per claim is skewed to the right with mean $150 and standard deviation $50. A random sample of 25 completed warranty claims is selected, and the sample mean cost is recorded. Suppose the process of selecting a random sample of 25 completed warranty claims and recording the sample mean cost is repeated for a total of 100 samples. Which of the following best describes a dotplot created from the 100 sample means?

(A) The dotplot has the same shape as the distribution of the population with mean $150 and standard deviation $25.
(B) The dotplot has the same shape as the distribution of the population with mean $150 and standard deviation $50.
(C) The dotplot has the same shape as the distribution of the population with mean $150 and standard deviation $100.
(D) The dotplot is closer to approximately normal than the distribution of the population with mean $150 and standard deviation $10.
(E) The dotplot is closer to approximately normal than the distribution of the population with mean $150 and standard deviation $50.

Answer 1

Answer: D. The dotplot is closer to approximately normal than the distribution of the population with mean $150 and standard deviation $10.

Explanation:

Based on the dotplot created from the 100 sample, the dotplot is closer to approximately normal than the distribution of the population with mean $150 and standard deviation $10.

The mean of the sampling distribution is just exactly like the population mean. On the other hand, the standard deviation will be: = 50/✓25 = 50/5 = 10

Therefore, the correct option is D.