I have the following problem:
"The breaking strength of a safety belt is known to be approximately normally distributed with a true mean (mu) of 8100 pounds and a true standard deviation (sigma) of 105 pounds. If a simple random sample of 40 belts is chosen, what is the probability that the sample mean (x-bar) will differ from the true mean (mu) by more than 30 pounds (in either direction)?"
I have an abnormally high z score, so I don't think I am doing it correctly.
n = 40 mu = 8100 sigma = 105
mu x-bar = 40
sigma x-bar = sigma/mu x-bar = 105/40 = 2.625
P(8070 < x-bar < 8130) = P((8070-40)/2.625 < z < (8130-40)/2.625) =
P(3059.05 < z < 3081.9)
Where have I gone wrong?