CNNBC recently reported that the mean annual cost of auto in

CNNBC recently reported that the mean annual cost of auto insurance is 996 dollars. Assume the standard deviation is 240 dollars. You take a simple random sample of 82 auto insurance policies.
Find the probability that a single randomly selected value is less than 965 dollars.
P(X < 965) =
Find the probability that a sample of size n=82 is randomly selected with a mean less than 965 dollars.
P(M < 965) =

Solution

Mean ( u ) =996
Standard Deviation ( sd )= 240/Sqrt ( 82 )
Number ( n ) = 82
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 965) = (965-996)/240/ Sqrt ( 82 )
= -31/26.5036= -1.1697
= P ( Z <-1.1697) From Standard NOrmal Table
= 0.1211