Q. 29 Mina is waiting in line at the D... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 2: Q. 29 (page 132)

Mina is waiting in line at the Department of Motor Vehicles (DMV). Her wait time of $32$ minutes is the $85^{t h}$ percentile of wait times. Is that good or bad? Write a sentence interpreting the $85^{t h}$ percentile in the context of this situation.

Short Answer

Expert verified

It would be bad for Mina to have to wait time at $85^{t h}$ percentile because $85 %$ of people had shorter wait time than Mina and only $15 %$ of people had larger wait times than Mina.

Step by step solution

Definition

In statistics, the percentiles are the partition values. Percentile divides the entire data into $100$ equal parts. The $50^{t h}$ percentiles denotes median and below this value lies $50 %$ of data. Similarly $60^{t h}$ percentile will have $60 %$ of data below it.

Explanation

The formula for finding the K^th percentile is:

$k^{t h} percentile = \frac{k (N + 1)}{100} t h item$

In the given situation, the Mina's waiting time is $32$ minutes, which is at $85^{t h}$ percentile value and it would not be good for mina as $85 %$ of people had shorter wait time than mina. In this context, mina would prefer a wait time corresponding to a lower percentile. The interpretation of the $85^{t h}$ percentile in the given context is $85 %$ of people at theDMVwaited $32$ minutes or less.