a. From National Weather Service records, the annual snowfall in the TopKick Mou

Question

a. From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 82 inches and a standard deviation ? of 12 inches. If the snowfall from 25 randomly selected years are chosen, what it the probability that the snowfall would be less than 85 inches?


b. The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 30. If 36 applicants are randomly chosen, what is the probability that they will have a rating between 230 and 250?

Please show work and how the answers was acquired. Thank you!

Explanation / Answer

1)From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of

82 inches and a standard deviation of 12 inches. If the snowfall from 25 randomly selected years

are chosen, what it the probability that the snowfall would be less than 85 inches?
z = (85-82)/(12/sqrt(25))
z = 1.25
prob(z < 1.25)
= 0.8944

2)

The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240

and the standard deviation is 30. If 36 applicants are randomly chosen, what is the probability that

they will have a rating between 230 and 250?
z(230) = (230-240)/(30/sqrt(36)) = -2
z(250) = (250-240)/(30/sqrt(36)) = 2
prob(-2 < z < 2)
= 0.9545

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