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?a Each day, a weather forecaster predicts whether or not

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 27E Chapter 2.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 27E

aProblem 27E

Each day, a weather forecaster predicts whether or not it will rain. For 80% of rainy days, she correctly predicts that it will rain. For 90% of non-rainy days, she correctly predicts that it will not rain. Suppose that 10% of days are rainy and 90% are non-rainy.

a. What proportion of the forecasts are correct?

b. Another forecaster always predicts that there will be no rain. What proportion of these forecasts are correct?

Step-by-Step Solution:

Step 1 of 3:

The experiment given here is of weather forecasting.

Let us define event  as a rainy day and event  as non rainy day.

And let event C denotes that the prediction i9s correct.

It is given that 10% of the days are rainy days. This implies P()=0.1.Also given that 90% of the days are non rainy days. This implies P()=0.9.

 And also it is given that P(correct prediction|it is a rainy day)=0.8 and P(correct prediction|it is a non rainy day)=0.9

That is P(C|)=0.8 and P(C|)=0.9.

Using these probability values we have to find the remaining probabilities.

Step 2 of 3:

(a)

Here we have to find the proportion of correct forecast. It is denoted by P(C).

This probability is given by,

P(C)=P(C|)*P()+ P(C|)*P()

       =(0.8*0.1)+(0.9*0.9)

       =0.08+0.81

       =0.89

Thus, the proportion of correct forecast is

Step 3 of 3

Chapter 2.3, Problem 27E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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