Question

CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars. Assume the standard deviation is 242 dollars. You take a simple random sample of 89 auto insurance policies.

Find the probability that a single randomly selected value is at least 980 dollars.
P(X > 980) =

Find the probability that a sample of size n=89n=89 is randomly selected with a mean that is at least 980 dollars.
P(M > 980) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 1016

standard deviation = = 242

a.

P(x 980) = 1 - P(x   980)

= 1 - P[(x - ) / (980 - 1016) / 242]

= 1 -  P(z -0.15)   

= 1 - 0.4404

= 0.5596

P(x 980) = 0.5596

b.

M = / n = 242 / 89 = 25.6519

P(M > 980) = 1 - P(M < 980)

= 1 - P[(M - M ) / M < (980 - 1016) / 25.6519]

= 1 - P(z < -1.40)

= 1 - 0.0808

= 0.9192

P(M > 980) = 0.9192