Homework question help please

Question

CNNBC recently reported that the mean annual cost of auto insurance is 1040 dollars. Assume the standard deviation is 280 dollars. You take a simple random sample of 70 auto insurance policies.

Find the probability that a single randomly selected value exceeds 972 dollars.

P(X > 972) =

Answer 1

Homework question help please

CNNBC recently reported that the mean annual cost of auto insurance is 1040 dollars. Assume the standard deviation is 280 dollars. You take a simple random sample of 70 auto insurance policies.

Find the probability that a single randomly selected value exceeds 972 dollars.

P(X > 972) =

Step-1

Given

Population mean mu = 1040

Population standard deviation sigma = 280

Sample size n = 70

Step-2

Standard error of the mean se = sigma/sqrt(n) = 280/sqrt(70) = 33.466

z-score of 972 = (972-1040)/33.466 = -2.03

 

Step-3

We have to find area under the standard normal curve to the right of 972 dollars >> right of -2.03

Approximately >> =(1.000-0.212) = 0.788