Question

NNBC recently reported that the mean annual cost of auto insurance is 1045 dollars. Assume the standard deviation is 278 dollars. You take a simple random sample of 92 auto insurance policies.

Find the probability that a single randomly selected value is less than 996 dollars.
P(X < 996) =

Find the probability that a sample of size n=92n=92 is randomly selected with a mean less than 996 dollars.
P(M < 996) =

Answer 1

Solution :

Given that ,

P(x < 996)

= P[(x - ) / < (996 - 1045) / 278]

= P(z < - 0.18)

Using z table,

= 0.4286

= 1045

= / n = 278 / 92 = 28.98

P( < 996) = P(( - ) / < (996 - 1045) / 28.98 )

= P(z < - 1.69)

Using z table

= 0.0455