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Q. 81

Introductory Statistics
Found in: Page 434
Introductory Statistics

Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

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Short Answer

81. The90th percentile sample average wait time (in minutes) for a sample of 100 riders is:

a. 315.0




The 90thpercentile sample average wait time for a sample of 100 riders is option "b" 40.3

See the step by step solution

Step by Step Solution

Step 1: Given information

Consider X be the continuous random variable which shows the waiting time is uniformly distributed. It should be expressed as:

X~U(0, 75)




Step 2:Final answer

Let's compute the average waiting time as follow:



=37.5 Minutes

Standard deviation of the given distribution is:




The sample size is greater than 30.

Hence, according to Central Limit Theorem

X¯~N37.5,21.650100 where, n=100

Step 3: Calculate the 90th percentile

Let's use Ti-83 calculator to compute the 90th percentile for sample average waiting time.

For this, Click on 2nd.

Then DISTR and scroll down to the invNorm option and enter the provided values of mean (37.5), standard deviation 21.65100 and the percentile,

After this, click on ENTER button of calculator to have the desired result.

The screenshot is given as below:

Therefore, 90th percentile sample average waiting time is approximately 40.27 hours.

Thus, the correct option is 'b'.

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