need clear and well written complete answer Prob 2. The annual rainfall for a ci

Question

need clear and well written complete answer

Prob 2. The annual rainfall for a city is assumed to be normally distributed with a mean of 100 cm,I and its mean t3 standard deviation values are estimated to be 160 and 40 cm, respectively (a) Calculate the standard deviation of the annual rainfall. (b) What is the probability that the rainfall will be less than 0? (c) What is the probability that the annual rainfall will be within the t3 standard deviation values? (d) Is normal distribution appropriate in this case?

Explanation / Answer

a) as 3 standard deviation away value =160

hence mean +3*std deviation =160

100+3*std deviation =160

hence std deviation =20

b) from normal distribution ; Z =(X-mean)/std deviation

hence probabilty that rainfall will eb less then 0=P(X<0)=P(Z<(0-100)/20)=P(Z<-5) =2.866*10-7

c)probabilty that rail fall will be between +/- 3 std deviation =P(-3<Z<3) =0.9986-0.0013 =0.9973

d)as probabilty of less then rain 0 is not exactly 0, it is not appropriate at that place.

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