Most weather forecasters protect themselves very well by attaching probabilities to their forecasts, such as “The probability of rain today is 40%.” Then, if a particular forecast is incorrect, you are expected to attribute the error to the random behavior of the weather rather than to the inaccuracy of the forecaster. To check the accuracy of a particular forecaster, records were checked only for those days when the forecaster predicted rain “with 30% probability.” A check of 25 of those days indicated that it rained on 10 of the 25.

a. If the forecaster is accurate, what is the appropriate value of p, the probability of rain on one of the 25 days?

b. What are the mean and standard deviation of x, the number of days on which it rained, assuming that the forecaster is accurate?

c. Calculate the z-score for the observed value, x = 10.

d. Do these data disagree with the forecast of a “30% probability of rain”? Explain.