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# ?a Each day, a weather forecaster predicts whether or not ## Problem 27E Chapter 2.3

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

##### ISBN: 9780073401331

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

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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.3 - Problem 27e

Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.3 - Problem 27e