SOLUTION: please help me solve this question CNNBC recently reported that the mean annual cost of auto insurance is 976 dollars. Assume the standard deviation is 298 dollars. You take a sim

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Question 1146801: please help me solve this question
CNNBC recently reported that the mean annual cost of auto insurance is 976 dollars. Assume the standard deviation is 298 dollars. You take a simple random sample of 77 auto insurance policies.
Find the probability that a single randomly selected value is less than 986 dollars.
P(X < 986) =
Find the probability that a sample of size
n
=
77
n=77
is randomly selected with a mean less than 986 dollars.
P(
¯¯¯
X
X¯
< 986) =

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
this is z
z=(x bar-mean)/sigma/sqrt (n)
this is (986-976)/298/sqrt (77)
or z < 10*sqrt(77)/298
z<+0.29
This has probability of 0.6141