ation from the American Institute of Insurance indicates that claims for a cost
ID: 3324453 • Letter: A
Question
ation from the American Institute of Insurance indicates that claims for a cost filed under auto insurance policies have a mean $19,400 and standard deviation $6,000 a. for all possible random samples of 50 claims, what is the shape of the sampling distribution of the sample means? (1 point) b. Specify the mean and standard deviation of the sampling distribution of the sample means, for samples of size 50 and mark appropriate values on the template below. (3 points) c What is the probability that in a random sample of 50 claims the mean amount of money claimed is more than $19,000? (4 points) What is the probability that in a random sample of 50 claims the mean amount of money claimed is less than $19,800? 4 points)Explanation / Answer
A) shape is bell shaped i.e. normal distribution
B) mean of sampling distribution = 19400
Standard deviation of sampling distribution = 6000/sqrt(50) = 848.53
C) P(X bar > 19000) = P(Z > (19000 - 19400) / 848.53)
= P(Z > - 0.47)
= 1 - P(Z < - 0.47)
= 1 - 0.3192
= 0.6808
D) P(X bar < 19800) = P(Z < (19800 - 19400)/848.53)
= P(Z < 0.47)
= 0.6808
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