Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P ( − b < z < b ) = 0.199 , find b. b =

Answer 1

Since the interval is symmetrical about z, there is the same area below and above the interval. The total area above and below would be 1 - 0.199 = 0.801. The area below would be 0.801/2 = 0.4005. So we just need to be z such that P(Z < z) = 0.4005, which is z = -0.252 and b = 0.252