Question

CNNBC recently reported that the mean annual cost of auto insurance is 1004 dollars. Assume the standard deviation is 278 dollars. You take a simple random sample of 55 auto insurance policies.

Find the probability that a single randomly selected value is less than 997 dollars. P(X < 997) =

Find the probability that a sample of size n = 55 is randomly selected with a mean less than 997 dollars. P( ¯ x < 997) =

Answer 1

Solution :

Given that ,

mean = = 1004

standard deviation = = 278

a) P(x < 997) = P[(x - ) / < (997 - 1004) / 278]

= P(z < -0.03)

Using z table,

= 0.4880

b) n = 55

=   = 1004

= / n = 278 / 55 = 37.49

P( < 997) = P(( - ) / < (997 - 1004) / 37.49)

= P(z < -0.19)

Using z table

= 0.4247