Question

In: Statistics and Probability

A weather forecaster predicts that the May rainfall in a local area will be between 2...

A weather forecaster predicts that the May rainfall in a local area will be between 2 and 9 inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed over the interval 2 to 9 inches.

(a) Calculate the expected May rainfall. (Round your answer to 1 decimal place.)

μx____ inches

(b) What is the probability that the observed May rainfall will fall within two standard deviations of the mean? Within one standard deviation of the mean? (Round all intermediate and final answers to 4 decimal places.)

Probability of May rainfall will fall within two SD
Probability of May rainfall will fall within one SD



ps, the other answers with this same problem are wrong.

Solutions

Expert Solution

X ~ U (2,9)

a) µ = (2 + 9) / 2 = 5.5

sd = (9 - 2) / sqrt(12) = 2.021

b) P(within 2 sd) = P(5.5 - 2 * 2.021 < X < 5.5 + 2 * 2.201)

                           = P(1.098 < X < 9.902)

                           = P(2 < X < 9)

                           = 1

P(within 1 sd) = P(5.5 - 1 * 2.021 < X < 5.5 + 1 * 2.201)

                      = P(3.479 < X < 7.521)

                      = (7.521 - 3.479) / (9 - 2)

                      = 0.5774

orchestra answered 2 years ago
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