Homework 25: The Standard Normal Distribution

1. Use a standard normal table to calculate \(\int_{-.44}^{1.33}e^{-z^2/2}\, dz\).
2. Let \(Z\) be a standard normal random variable. Find the following probabilities:
   1. \(P(0\leq Z\leq 2.07)\)
   2. \(P(Z>-1.06)\)
   3. \(P(Z\leq -2.33)\)
   4. \(P(-.33\leq Z\leq 1.2)\)
3. Assume that \(Z\) is a standard normal random variable. For what values of \(z\) are the following statements true?
   1. \(P(Z\leq z)=0.33\)
   2. \(P(-1.00\leq Z\leq z)=0.564\)
   3. \(P(-z\leq Z\leq z)=0.8\)