SOLUTION: CNNBC recently reported that the mean annual cost of auto insurance is 1040 dollars. Assume the standard deviation is 293 dollars. You take a simple random sample of 84 auto insura

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Question 1133983: CNNBC recently reported that the mean annual cost of auto insurance is 1040 dollars. Assume the standard deviation is 293 dollars. You take a simple random sample of 84 auto insurance policies.
(a) Find the probability that a single randomly selected value is less than 994 dollars.
P(X < 994) =

(b) Find the probability that a sample of size n=84 is randomly selected with a mean less than 994 dollars.
P(M < 994) =

Enter your answers as numbers accurate to 4 decimal places.
Answer by Glaviolette(140) About Me  (Show Source):
You can put this solution on YOUR website!
I am assuming the data is normally distributed. If so, z scores can be used to solve. Otherwise, I don't believe the problem can be solved.
a. z = (994 - 1040)/293 = -.16
Using a z-score table P(X < 994) = .4364
b. z = (994 - 1040)/(293/sq rt 84) = -1.44
Using a z-score table M(X < 994) = .0749