Chapter 18, Problem 40E

(a)

To determine

To explain why you suspect this distribution may be skewed to the right.

Explanation of Solution

It is given in the question that some business analyst estimated that the length of time people work at a job has mean of $6.2$ years and a standard deviation of $4.5$ years. Thus, the distribution of length of time people work at a job is likely to be skewed to the right because some people stay at the same job for much longer than the mean plus two or three standard deviations. Additionally, the left tail cannot be long, because a person cannot work at a job for less than zero years.

(b)

To determine

To explain why you could estimate the probability that $100$ people selected at random had worked for their employers an average of ten years or more, but you could not estimate the probability that an individual has done so.

Answer to Problem 40E

Explanation of Solution

It is given in the question that some business analyst estimated that the length of time people work at a job has mean of $6.2$ years and a standard deviation of $4.5$ years. Thus, we can estimate the probability that $100$ people selected at random had worked for their employers an average of ten years or more, but you could not estimate the probability that an individual has done so because the Central Limit Theorem guarantees that the distribution of the mean time is Normally distributed for large sample sizes, as long as the assumptions and conditions are satisfied. The CLT doesn’t help us with the distribution of individual times.