Most weather forecasters protect themselves extremely well by attaching probabilities to their forecasts, such as "The probability of rain today is 40%." Then, if a specific forecast is incorrect, you're expected to attribute the error to the random behavior of the weather rather than to the inaccuracy of forecaster. To check the accuracy of specific 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 25.
a. If the forecaster is accurate, determine the approximate value of p, the probability of rain on one of the 25 days?
b. Determine the mean and standard deviation of x, the number of days on which it rained, supposing that the forecaster is accurate?
d. Do these data disagree with forecast of a"30% probability of rain"? Discuss.