Question

CNNBC recently reported that the mean annual cost of auto insurance is 961 dollars. Assume the standard deviation is 237 dollars. You take a simple random sample of 94 auto insurance policies.

Find the probability that a single randomly selected value is more than 964 dollars.
P(X > 964) =

Find the probability that a sample of size n=94n=94 is randomly selected with a mean that is more than 964 dollars.
P(M > 964) =

Answer 1

Solution :

Given that ,

mean = = 961

standard deviation = = 237

(a)

P(x > 964) = 1 - P(x < 964)

= 1 - P((x - ) / < (964 - 961) / 237)

= 1 - P(z < 0.0127)

= 1 - 0.5051   

= 0.4949

P(x > 964) = 0.4949

Probability = 0.4949

(b)

n = 94

= 961 and

= / n = 237 / 94

P(M > 964) = 1 - P(M < 964)

= 1 - P((M - ) /   < (964 - 961) / 237 / 94 )

= 1 - P(z < 0.1227)

P(M > 964) = 1 - 0.5488 = 0.4512

Probability = 0.4512