A population has a mean of 78 with a standard deviation of 9.8

a.) What is the probability that one element of the population selected at random is between 72 and 91?

b.) What is the probability that a random sample of 36 from this population has a sample mean between 77 and 79?

Pr (72<x<91) = pr (-6/9.8<z<13/9.8) = pr (-0.61<z<1.33) = P(Z<1.33)-P(Z<-0.61) = 0.908-0.271 = 0.637

b) std = 9.8/6 = 1.633

Pr(77<x<79) = pr ((77-78)/1.63<z<79-78/1.63) = Pr(-0.613<z<0.613) = 0.729-0.271 = 0.459

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