SOLUTION: The mean annual cost of automobile insurance is R95. Assume that the population standard deviation is R14. What is the probability that a simple random sample of size 30 for automo

Question 1183214: The mean annual cost of automobile insurance is R95. Assume that the population standard deviation is R14. What is the probability that a simple random sample of size 30 for automobile insurance policies will have a sample mean less than R90
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
this is a z-test with z=(x bar-mean)/sigma/sqrt (n)
z < (90-95)/14/sqrt(30)
z < -5*sqrt(30)/14 inverting and multiplying to deal with division.
z < -1.956
0.0252 is probability
The sd of the sampling distribution is 14/sqrt(30) or 2.556
Then it is z < -5/2.556
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