Question

**ASAP**

CNNBC recently reported that the mean annual cost of auto insurance is 975 dollars. Assume the standard deviation is 298 dollars. You take a simple random sample of 58 auto insurance policies.

Find the probability that a single randomly selected value is less than 987 dollars.
P(X < 987) =

Find the probability that a sample of size n=58n=58 is randomly selected with a mean less than 987 dollars.
P(M < 987) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Solution :

Given that ,

a) P(x < 987 )

= P[(x - ) / < (987 - 975) / 298]

= P(z < 0.04)

Using z table,

= 0.5160

b) = 975

= / n = 298 / 58

P(M < 987) = P((M - ) / < (987 - 975) / 298 / 58 )

= P(z < 0.31)

Using z table

= 0.6217