Question

To check the accuracy of a particular weather forecaster, records were checked only for those days when the forecaster predicted rain "with 20% probability." A check of 15 of those days indicated that it rained on 5 of the 15.

(a)

If the forecaster is accurate, what is the appropriate value of p, the probability of rain on one of the 15 days?

p =

(b)

What are the mean μ and standard deviation σ of x, the number of days on which it rained, assuming that the forecaster is accurate? (Round your standard deviation to two decimal places.)

(c)

Calculate the z-score for the observed value, x = 5. [HINT: Recall that z-score = (x − μ)/σ.] (Round your answer to two decimal places.)

z =

(d)

Do these data disagree with the forecast of a "20% probability of rain"? Explain.

The observed event is less than 2 standard deviations above the mean, so it is very unlikely assuming p is accurate.

The observed event is less than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate.     

The observed event is more than 2 standard deviations above the mean, so it is unlikely assuming p is accurate.

The observed event is more than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate.

Answer 1