Question

CNNBC recently reported that the mean annual cost of auto insurance is 960 dollars. Assume the standard deviation is 213 dollars. You take a simple random sample of 70 auto insurance policies. Find the probability that a single randomly selected value is less than 995 dollars. P(X < 995) = Find the probability that a sample of size n = 70 is randomly selected with a mean less than 995 dollars. P(M < 995) =

Answer 1

Assuming that the cost of auto insurance follows Normal distribution with mean = 960 and standard deviation = 213

X ~ Normal(960, 213²)

Now,

The probability that a single randomly selected value is less than 995 dollars

Let M denotes the mean annual cost of auto insurance of a sample of size n = 70.

or

The probability that a sample of size n = 70 is randomly selected with a mean less than 995 dollars

(ans)