Question

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever...

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)

a) P(0 <= Z <= 2.73)

b) P(Z <= 1.63)

c) P(-1.05 <= Z)

d) P(|Z| <= 2.5)

How do you do this or is there an easy way you can do this in excel?

Homework Answers

Answer #1

We use Standard Normal Distribution as Z is given

a) Can be written as P(z<=2.73)-P(z<=0), this is a difference between two cumulative probabilities. Easiest way to solve this using excel is to type =NORM.S.DIST(2.73)-NORM.S.DIST(0) which gives 0.4968332837

b) =NORM.S.DIST(1.63) = 0.9484492515

c) P(-1.05 <= Z) is same as P(Z>=-1.05) or 1-P(z<=1.05) =1-NORM.S.DIST(1.05) = 0.1468590564

d) P(|Z| <= 2.5) = P(-2.5 <=Z<=2.5) or P(Z<=2.5)-P(Z<-2.5)=2*P(Z<2.5)-1=2*NORM.S.DIST(2.5)-1 = 0.9875806693

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