Find the probability that a sample of size n = 85 is randomly selected with a mean less than 970 dollars. P(M < 970) =

Question

CNNBC recently reported that the mean annual cost of auto insurance is 975 dollars. Assume the standard deviation is 245 dollars. You take a simple random sample of 85 auto insurance policies.

Answer 1

P(M < 970), where M is normal with mean 975 and SD 245

translate M to standard normal (z) with mean 0 and SD 1 using formula:

z = (M - population mean)/(SD/sqrt(sample size))

P(z < (970 - 975)/(245/sqrt(85))

P(z < -0.19) = 0.4247