Elementary Statistics Departmental Final Exam Part l(Form B) Problem #3 (12 poin

Question

Elementary Statistics Departmental Final Exam Part l(Form B) Problem #3 (12 points) Information from the American Institute of Insurance indicates that claims for a cost fled unae auto insurance policies have a mean $19,400 and standard deviation $6,000 e roll s as the olled profit a. For all possible random samples of 50 claims, what is the shape of the sampling distribution of the sample means? oint) (1 point) s) 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) 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) c. 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) d. ho your work. Partial credit will be given.

Explanation / Answer

a) as sample size n>=30 ; therefore shape should be normal from central limit theorum with mean =19400

and std error of mean =std deviation/(n)1/2 =6000/(50)1/2 =848.5281

b) mean =19400

std deviation =848.5281

and as these points are distriuted -std deviation to +3 deviation from mean mark them like this:

from left to right:

c)P(X>19000)=P(Z>(19000-19400)/848.528)=P(Z>-0.4714)=1-P(Z<-0.4714)=1-0.3187 =0.6813

d)P(X<19800)=P(Z<0.4714)=0.6813

16854.42 17702.94 18551.47 19400 20248.53 21097.06 21945.58 22794.11

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