Chapter 4.1, Problem 44E

(a)

To determine

To explain what $95\text{th}$ percentile means in this setting.

Explanation of Solution

In the question it is given that some internet service providers charge companies based on how much bandwidth they use in a month. So, one method the ISPs use for calculating bandwidth is to find the $95\text{th}$ percentile of a company usage based on the sample of hundreds during a month. Thus, in this setting the $95\text{th}$ percentile means is the bandwidth for which he company uses less than this bandwidth $95\%$ of the time. Thus, the company uses a bandwidth smaller than the $95\text{th}$ percentile $95\%$ of the time.

(b)

To determine

To explain which would cost a company more: the $95\text{th}$ percentile method or a similar approach using the $98\text{th}$ percentile.

Answer to Problem 44E

Using the $98\text{th}$ percentile would cost the company more.

Explanation of Solution

In the question it is given that some internet service providers charge companies based on how much bandwidth they use in a month. So, one method the ISPs use for calculating bandwidth is to find the $95\text{th}$ percentile of a company usage based on the sample of hundreds during a month. Thus, a similar approach using the $98\text{th}$ percentile would cost the company more because the bandwidth will be higher for the $98\text{th}$ percentile than for the $95\text{th}$ percentile and a higher bandwidth will cost more.