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.

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.

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.

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.

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.