Question

Within a normal distribution, the sample mean is equal to 3.0. At the 43.32% point within the distribution, the critical value is equal to ______ . Thus the critical boundary will be equal to +_________ and -_______.

Answer 1

We want to find, z-score such that, P(-z < Z < z) = 0.4332

P(-z < Z < z) = 0.4332

=> 2 * P(Z < z) - 1 = 0.4332

=> 2 * P(Z < z) = 1 .4332

=> P(Z < z) = 0.7166

Using standard normal z-table we get, z-score corresponds to probability 0.7166 (or nearest probability)  is, z = 0.57

=> Crotical value = 0.57

Thus the critical boundary will be equal to +0.57 and -0.57