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·IIT-Mobile 4:47 PM 88%- Done 8 of 10 Elementary Statistics Departmental Final x

ID: 3322632 • Letter: #

Question

·IIT-Mobile 4:47 PM 88%- Done 8 of 10 Elementary Statistics Departmental Final xam Part i (Form ) Em Problem #3 (12 points) nformation 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 SO 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 on the template below means, for samples of size 50 and mark appropriate values on the (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) d. What is the probability that in a random sample of 50 claims the mean amount of 4 points) money claimed is less than $19,800

Explanation / Answer

a) as sample size is greater than 30 therfore from central limit theorum shape of sampling distirbution of mean will be approximately normal

b)

mean =19400

std deviaiton of sampling distirbution of mean =std deviaiton/(n)1/2 =6000/(50)1/2 =848.528

in templete middle value =19400

as point are located -3,-2,-1,0,1,2,3 std deviaiton away from mean

hence values from left side =16854.42 ; 17702.94 ; 18551.47 ;19400 ; 20248.53 ; 21097.06 ; 21945.58

c)P(Xbar>19000)=1-P(Xbar<19000)=1-P(Z<(19000-19400)/848.53)=1-P(Z<-0.4714)1=1-0.3187 =0.6813

d)P(Xbar<19800)=P(Z<((19800-19400)/848.53)=P(Z<0.4714)=0.6813