Need all answers a, b, c and D.... Thank you! al Pinat Exam Part it (Form AlEmpl

Question

Need all answers a, b, c and D.... Thank you!

al Pinat Exam Part it (Form AlEmpliD: Problem #3 (12 points) information from the American Institute of Insurance indicates that the amount of life insurance per household in the United States is normally distributed with mean $110,000 and standard deviation $40,000 For all possible random samples of 25 households, 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 25. b. (3 points) What is the likelihood that a random sample of 25 households the mean cost of life insurance is less than $100,000? c. (4 points) What is the likelihood that in a random sample of 25 households the mean cost of life insurance is more than $120,000? b. (4 poi

Explanation / Answer

A)Using Central limit theorem the distribution of sample mean of a normal distribution follows a normal distribution. Thus, the shape is bell shaped.

B)For a sample of 25 the mean is same as population mean $110000 and the standard deviation is 40000/sq rt 25=8000

C)For X=100000, z=(x-)/=(100000-110000)/8000=-1.25

P(X<100000)=P(z<-1.25)=0.1056

D)ForX=120000, z=(120000-110000)/8000=1.25

P(X>120000)=P(z>1.25)=0.8944

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