Section 5.4: SamplingDistribution and the Central Limit Theorem 5. Find the prob

Question

Section 5.4: SamplingDistribution and the Central Limit Theorem

5. Find the probabilities.

(References: example 5 and 6page 276 - 277, end of section exercises 25 - 31 pages 280 -281)

a.    From National Weather Service records, theannual snowfall in the TopKick Mountains has a mean of 92 inchesand a standard deviation s of 12 inches. If the snowfall from 25randomly selected years are chosen, what it the probability thatthe snowfall would be greater than 95 inches?

(5 points)

b.    The loan officer rates applicants for credit.Ratings are normally distributed. The mean is 240 and the standarddeviation is 60. If 36 applicants are randomly chosen, what is theprobability that they will have a rating between 220 and 260? (5 points)

Explanation / Answer

part b)
Mean = 240 and SD = 60

Then SE = 60/sqrt(36) = 10

P(230 < X < 260) = P( (230-240)/10 < Z <(260-240)/10)
= P(-1 < Z < +2)
= P(-1 < Z) - P(+2 < Z)
= 0.84134 - 0.02275
= 0.81859

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