Chapter 6.7, Problem 6E

To determine

To predict: the number of days over the course of a year for which the forecast will be correct.

Answer to Problem 6E

For 267 days over the course of year the forecast will be correct.

Explanation of Solution

Given information :

Consider, the information provided in the question,

The forecast is correct 22 times in a month of 30 days.

Calculation :

Here, total number of trials is 30. And, and number of success that the forecast is correct is 22.

Now, the experimental probability that the forecast is correct is

  $\begin{array}{l}P\left(\text{Forecast is correct}\right)=\frac{\text{Number of success}}{\text{Number of trials}}\\ P\left(\text{Forecast is correct}\right)=\frac{\text{22}}{\text{30}}\\ P\left(\text{Forecast is correct}\right)=\frac{\text{22}}{\text{30}}\end{array}$

Multiply the experimental probability by number of days in a year i.e. 365 to predict how many days the forecast will be correct over the course of a year. Therefore,

  $\frac{\text{22}}{\text{30}}\times 365\approx 267$

Hence,

For 267 days over the course of year the forecast will be correct.