Suppose that the yearly rainfall totals for a city in northern California follow a normal distribution, with mean of 18 inches and standard deviation of 6 inches. In each part, find a z-score and then find the desired probability using a normal curve table as an aid. Then redo the calculation with R in two ways with the z-score and on the original scale. For a cumulative probability for a z-score, the syntax for P(Z<=k) is pnorm(k). The cumulative probability P(X<=k) for a generic Normal RV with mean mu and standard deviation s can be found in R using pnorm(k,mu,s), where youre entering numbers for mu and s. Report the value from R to five decimal places to see how it differs from the book.

What is the amount of rain that only 20% of all years will experience?

And....

Suppose that the amount that students at University slept last night is a normal random variable with mean = 7 hours and standard deviation = 1.5 hours.

What is the amount of sleep that only 2.5% of students sleep less than? What is the amount of sleep that only 9% of students sleep more than?