Question

CNNBC recently reported that the mean annual cost of auto insurance is 1045 dollars. Assume the standard deviation is 219 dollars. You take a simple random sample of 59 auto insurance policies.

Find the probability that a single randomly selected value is less than 979 dollars.
P(X < 979) =

Find the probability that a sample of size n=59n=59 is randomly selected with a mean less than 979 dollars.
P(M < 979) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

a) The probability that a single randomly selected value is less than 979 dollars is P(X < 979) = 0.3816

Given

b)  The probability that a sample of size n=59 is randomly selected with a mean less than 979 dollars is
P(M < 979) = 0.0103