Question

CNNBC recently reported that the mean annual cost of auto insurance is 1048 dollars. Assume the standard deviation is 229 dollars. You take a simple random sample of 85 auto insurance policies.

Find the probability that a single randomly selected value exceeds 971 dollars.
P(X > 971) =

Find the probability that a sample of size n=85 is randomly selected with a mean that exceeds 971 dollars.
P(M > 971) =

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.5 years, and standard deviation of 1.8 years.

If you randomly purchase 12 items, what is the probability that their mean life will be longer than 8 years?

Answer 1