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 4 and 8 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 4 to 8 inches. (a) Calculate the expected May rainfall. (Round your answer to 1 decimal place.) mu_x 6 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 a intermediate and final answers to 4 decimal places.) Probability of May rainfall will fall within two SD 0.5774 Probability of May rainfall will fall within one SD 1

Explanation / Answer

for uniform distribution mean =(4+8)/2 =6

std deviation =(8-4)/(12)1/2 =1.1547

hence probabilty that fall in 2 SD =P(3.69<X<8.30)=1 (as contain whole range)

hence probabilty that fall in 1 SD =P(4.8453<X<7.1547)=0.5774 (as contain whole range)

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