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 7 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 7 inches. 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

The question clearly mentions the UNIFORM distribution and so the Normal distribution has nothing to do with it.

For a uniform continuous distribution the standard deviation is
s = (top value - bottom value)/sqrt(12)

So in this case it is (6 - 3)/sqrt(12) = 0.866

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

For one standard deviation each side
(2*0.866)/3 = 0.5773

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