Question

CNNBC recently reported that the mean annual cost of auto insurance is 989 dollars. Assume the standard deviation is 294 dollars. You take a simple random sample of 75 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 = 75 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

Let us consider that the cost of auto insurance be Normally distributed and it is denoted by X. Then we can write as,

X~

Note: It is not mentioned in the question, that cost of auto insurance be Normally distributed but I have assumed because it is given that the standard deviation is 294 which is for the population i.e. population standard deviation. Since we have the population mean and population standard deviation. That's why one can assume the distribution is normal.