To check the accuracy of a particular weather forecaster, records were checked o
ID: 3333084 • Letter: T
Question
To check the accuracy of a particular weather forecaster, records were checked only for those days when the forecaster predicted rain "with 40% probability." A check of 25 of those days indicated that it rained on 11 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?
p =
(b) What are the mean and standard deviation 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 = 11. [HINT: Recall that z-score = (x )/.] (Round your answer to two decimal places.)
z =
(d) Do these data disagree with the forecast of a "40% probability of rain"? Explain.
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 pis 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 less than 2 standard deviations above the mean, so it is very unlikely assuming p is accurate.
= days = daysExplanation / Answer
a) P = 25C1 * 0.4^1 * 0.6^24
P = 0.0000484
b)
c) z = (11 - 10)/2.45
z = 0.41
d) The observed event is less than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate.
= n * p = 0.4 * 25 = 10 days = V(n * p * q) = 2.45 daysRelated Questions
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