Question

CNNBC recently reported that the mean annual cost of auto insurance is 1048 dollars. Assume the standard deviation is 211 dollars. You take a simple random sample of 94 auto insurance policies.

Find the probability that a single randomly selected value is less than 962 dollars.

P(X < 962) =

Find the probability that a sample of size n=94 is randomly selected with a mean less than 962 dollars.
P(M < 962) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

a)

Given,

= 1048 , = 211

We convert this to standard normal as

P( X < x) = P( Z < x - / )

So,

P( X < 962) = P( Z < 962 - 1048 / 211)

= P( Z < -0.4076)

= 0.3418

b)

Using central limit theorem,

P( M < x) = P( Z < x - / / sqrt(n) ) )

So,

P( M < 962) = P (Z < 962 - 1048 / 211 / sqrt(94) ) )

= P( Z < -3.9517)

= 0