Question

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

a. Explain what “$95\mathrm{th}$percentile” means in this setting.

b. Is it possible to determine the z-score for a usage total that is at the $95\mathrm{th}$percentile? If so, find the z-score. If not, explain why not

Short answer

Part(a) This means that the $95th$percentile bandwidth is the bandwidth that the company consumes less than $95\%$of the time.

Part(b) Yes, The z-score is $98\mathrm{th}$percentile.

Step-by-step solution

Part(a) Step 1 : Given information

We need to explain $95\mathrm{th}$ percentile in this setting.

Part(a) Step 2 : Simplify

Some internet service providers (ISPs) bill businesses based on the amount of bandwidth they consume every month.
As a result, we need to figure out what the $95\mathrm{th}$ percentile means in this situation.
This means that the $95\mathrm{th}$percentile bandwidth is the bandwidth that the company consumes less than $95\%$ of the time.
$95$percent of the time, the company utilises bandwidth that is less than the $95\mathrm{th}$ percentile.

Part(b) Step 1 : Given information

We need to find z-score for the given data.

Part(b) Step 2 : Simplify

The z-score for a usage total that is in the $95\mathrm{th}$percentile can be calculated.
And the bandwidth's z-score will be $98\mathrm{th}$percentile, because bandwidth for the $98\mathrm{th}$percentile will be higher than for the $95\mathrm{th}$percentile, and higher bandwidth will cost more.
As a result, the outcome.