A weather forecaster predicts that the May rainfall in a local area will be betw

Question

A weather forecaster predicts that the May rainfall in a local area will be between 1 and 5 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 1 to 5 inches.

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

x 3.0 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 ??

Explanation / Answer

Standard deviation of uniform distribution, SD = (b-a)/12 = (5-1)/12 = 1/3

For a uniform distribution the probability between any two values is their difference divided by the whole interval

Probability of May rainfall will fall within two SD = P(3-(2*0.3333) < X < 3+(2*0.3333)) = P(2.3333 <X < 3.6667)
= (3.6667 - 2.3333)/4 = 0.3333

Probability of May rainfall will fall within one SD = P(3-0.3333 < X < 3+0.3333) = P(2.6667 <X < 3.3333)
= (3.3333 - 2.6667)/4 = 0.1667

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