Departmental Final Exam Part II (Form B) EmplID: Problem #3 (12 points) Informat

Question

Departmental Final Exam Part II (Form B) EmplID: Problem #3 (12 points) Information 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 For all possible random samples of 50 claims, what is the shape of the sampling distribution of the sample means? a. 1 point) 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. b. (3 points) 7 What is the probability that in a random sample of 50 claims the mean amount of money claimed is more than $19,000? c. 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? d. 4 points) Show your work. Partial credit will be given.

Explanation / Answer

(a)

According to the Central Limit Theorem, the sampling distribution of sample means always has a normal distribution irrespective of the nature of the parent distribution from which the samples ae drawn.

(b)

Using relation:

SE = S/n0.5

Here,

SE = Standard error of the mean = Standard deviation of the sampling distribution

Putting values:

SE = 6000/500.5 = 848.53

(c)

The corresponding z-score for this case is:

z = (X-m)/SE = (19000-19400)/848.53 = -0.471

The corresponding p-value for this z-score is:

p = 0.319

So, the reqd probability is: 1-p = 1-0.319 = 0.681

(d)

The corresponding z-score for this case is:

z = (X-m)/SE = (19800-19400)/848.53 = 0.471

The corresponding p-value for this z-score is:

p = 0.681

Hope this helps !

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