Question

Internet charges $(2.1)$ Some Internet service providers (ISPs) charge companies based on how much bandwidth they use in a month. One method that ISPs use for calculating bandwidth is to find the $95th$ percentile of a company’s usage-based on samples of hundreds of $5$-minute intervals during a month.

(a) Explain what “$95th$ percentile” means in this setting.

(b) Which would cost a company more: the $95th$ percentile method or a similar approach using the

98th percentile? Justify your answer.

Short answer

Part (a) $95$ percent of the time, the company utilises bandwidth that is less than the $95th$ percentile.

Part (b) Using the $98th$percentile would cost the company more.

Step-by-step solution

 Part (a) Step 1: Given information

ISPs charge businesses by calculating the bandwidth equal to the $95th$ percentile of a company's consumption based on hundreds of $5-$minute intervals over the course of a month.

Part (a) Step 2: Concept

A simple random sample (SRS) of size $n$ is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

Part (a) Step 3: Explanation

As indicated in the question, Some internet service providers bill businesses based on their monthly bandwidth usage. As a result, one way used by ISPs to calculate bandwidth is to find the $95th$percentile of a company's usage based on a sample of hundreds over the course of a month. As a result, in this case, the $95th$percentile represents the bandwidth that the company consumes less than $95$percent of the time. As a result, the organization frequently utilizes bandwidth that is less than the $95th$percentile.

Part (b) Step 1: Explanation

Some internet service providers charge businesses based on how much bandwidth they use per month, as stated in the question. As a result, one way used by ISPs to calculate bandwidth is to find the $95th$ company usage from a sample of hundreds over the course of a month. As a result, a similar method employing the $98th$ percentile will cost the organisation more because bandwidth for the $98th$ percentile will be higher than for the $95th$ percentile, and more bandwidth costs more.