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Chapter 5: Q4E (page 315)

Find the 0.25 and 0.75 quantiles of the Fahrenheit temperature at the location mentioned in Exercise 3.

Short Answer

Expert verified

0.25 quantile is 65.302

0.75 quantile is 70.698

Step by step solution

01

Given information

At a certain location the temperature in degrees Fahrenheit at a certain location is normally distributed with mean 68 degrees and standard deviation is 4 degrees.

02

Calculating Quantiles of the Fahrenheit Temperature 

The q quantile of the temperature in degrees Fahrenheit:

\(68 + 4{\phi ^{ - 1}}\left( q \right).\)

We have

\({\phi ^{ - 1}}\left( {0.75} \right) = 0.6745\)

\({\phi ^{ - 1}}\left( {0.25} \right) = - 0.6745\)

Hence

The 0.25 quantile is 65.302

The 0.75 quantile is 70.698

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