(3 points) An automobile insurer has found that repair claims are Normally distr

Question

(3 points) An automobile insurer has found that repair claims are Normally distributed with a mean of S680 and a standard deviation of $620. (a) Find the probability that a single claim, chosen at random, will be less than $630. ANSWER: (b) Now suppose that the next 100 claims can be regarded as a random sample from the long-run claims process. Find the probability that the average is smaller than $630 ANSWER: of the 100 claims (c) If a sample larger than 100 claims is considered, there would be "LESS", "MORE" or "AN EQUAL" without the quotes.) chance of getting a sample with an average smaller then $630. (NOTE: Enter

Explanation / Answer

mean = 680
std. dev. = 620

(a)
P(X < 630) = P(z < (630 - 680)/620) = P(z < -0.08064) = 0.4679

b)
P(X < 630) = P(z < (630 - 680)/(620/sqrt(100)) = P(z < -0.8065) = 0.21

c)

Less chance of getting sample

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