SOLUTION: CNNBC recently reported that the mean annual cost of auto insurance is 1034 dollars. Assume the standard deviation is 224 dollars. You take a simple random sample of 83 auto insura

Question 1170283: CNNBC recently reported that the mean annual cost of auto insurance is 1034 dollars. Assume the standard deviation is 224 dollars. You take a simple random sample of 83 auto insurance policies.
Find the probability that a single randomly selected value is less than 998 dollars.
P(X < 998) =

Find the probability that a sample of size
n
=
83
is randomly selected with a mean less than 998 dollars.
P(M < 998) =

Enter your answers as numbers accurate to 4 decimal places
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd=-36/224
that probability off z < that value is 0.4362
-
z=(x-mean)/sigma/sqrt(n), assuming the sd is known for the population, which it likely is here.
z < (998-1034)/224/sqrt(83)
=-36*sqrt(83)/224=-1.464
that probability is 0.0716.

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