Question

CNNBC recently reported that the mean annual cost of auto insurance is 952 dollars. Assume the standard deviation is 294 dollars. You take a simple random sample of 80 auto insurance policies.

Find the probability that a single randomly selected value is less than 977 dollars.

P(X < 977) =

Find the probability that a sample of size n = 80 is randomly selected with a mean less than 977 dollars.

P(M < 977) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Solution :

Given that,

mean = = 952

standard deviation = = 294

a ) P( x < 977 )

P ( x - / ) < ( 977 - 952 / 294 )

P ( z < 25 / 294 )

P ( z < 0.08 )

= 0.5319

Probability = 0.5319

b ) n = 80

=  952

₌ / n = 294 80 = 32.8702

P( < 977 )

P (   - / ) < ( 977 - 952 / 32.8702 )

P ( z < 25 / 32.8702 )

P ( z < 0.76 )

= 0.7764

Probability = 0.7764