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

a. 315.0

b.40.3

c.38.5

d.65.2

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

X~U(0,75)

Where,

a=0

b=75

02

Step 2:Final answer

Let's compute the average waiting time as follow:

μx=b-a2

=75-02

=37.5Minutes

Standard deviation of the given distribution is:

σx=(b-a)212

=(75-0)212

=21.650

The sample size is greater than 30.

Hence, according to Central Limit Theorem

X¯~N37.5,21.650100where,n=100

03

Calculate the 90th percentile

Let's use Ti-83 calculator to compute the 90thpercentile 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 21.65100and the percentile,

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

The screenshot is given as below:

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

Thus, the correct option is 'b'.

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