#3 (12 points) Part auto insurance policies have a mean $19,400 and standard dev

Question

#3 (12 points) Part auto insurance policies have a mean $19,400 and standard deviation a. For all possible random samples of 50 claims, whet distribution of the sample means? is the shape of the sampiee b. Specify the mean and standard deviation of the sampling dist means, for samples of size 50 and mark appropriate values on the distribution of the sample template below. (3 points) . What is the probability that in a random sample of SO 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? d. (4 points) Show your work. Partial credit will be given.

Explanation / Answer

a) as sample size is >30 therefore from central limit theorum shape of distribution of sampling mean will be approximately normal

b) mean =19400 and std errorr of mean =std deviaiton/(n)1/2 =6000/(50)1/2 =848.528

for marks are -3 std deviation to 3 std deviaiton from mean ; put this values on marks from left to right:

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

d)probabaility =P(X<19800)=(Z<(19800-19400)/848.528)=P(Z<0.4714) =0.6813

16854.42 17702.94 18551.47 19400 20248.53 21097.06 21945.58

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