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

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) (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
RELATED QUESTIONS
CNNBC recently reported that the mean annual cost of auto insurance is 1040 dollars.... (answered by Boreal)

CNNBC recently reported that the mean annual cost of auto insurance is 1046. Assume the... (answered by Boreal)

CNNBC recently reported that the mean annual cost of auto insurance is 1034 dollars.... (answered by Boreal)

CNNBC recently reported that the mean annual cost of auto insurance is 1002 dollars.... (answered by Boreal)

CNNBC recently reported that the mean annual cost of auto insurance is 1027 dollars.... (answered by Boreal)

CNNBC recently reported that the mean annual cost of auto insurance is 1025 dollars.... (answered by CPhill)

CNNBC recently reported that the mean annual cost of auto insurance is 1046 dollars.... (answered by Boreal)

I need help solving the following question with a calculator and how to type it in... (answered by Boreal)

CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars.... (answered by Boreal)