.Suppose the yearly rainfall total Y for a city in northern California follows a

Question

.Suppose the yearly rainfall total Y for a city in northern California follows a normal distribution, with a mean of 18 inches and a standard deviation of 6 inches.

(a) For each of the following probabilities, draw the density curve corresponding to the distribution and shade in the area under the curve corresponding to the desired probability. Use R Commander to calculate each probability.

i. P(Y < 9)

ii. P(Y 18)

iii. P(15 < Y < 23)

(b) Find the z-score for Y = 9.

(c) Suppose that in a given year, the total rainfall is only 9 inches. You work for the local newspaper, and your editor has asked you to write a story about the terrible drought the town is suffering and how abnormal the situation is. Write a few sentences that you could use to explain the statistical facts to your readers (and your editor). Be sure to comment on whether or not you agree that the situation is terribly abnormal.

Explanation / Answer

i

Z=(Y-MIU)/(6/sqrt(n)

Z=(9-18)/(6)

Z=-1.5

P(Y < 9) =0.066

ii

Z=(Y-MIU)/(6/sqrt(n)

Z=(18-18)/(6)

Z=0

P(Y 18) =0.5

iii

Z=(Y-MIU)/(6/sqrt(n)

Z=(15-18)/(6)

Z=-0.5

Z=(Y-MIU)/(6/sqrt(n)

Z=(23-18)/(6)

Z=0.833

  P(15 < Y < 23)=0.4891

(b) Find the z-score for Y = 9.

-1.5

c) its normal abnormal because the probability to be 9 or lower is 0.07

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