Chapter 7.2, Problem 17E

Applet Exercise Refer to Example 7.4. Use the applet Chi-Square Probabilities and Quantiles to find $P\left({\displaystyle {\sum }_{i=1}^6{Z}_i^2\le 6}\right)$. (Recall that $P{\displaystyle {\sum }_{i=1}^6{Z}_i^2}$ has a χ² distribution with 6 df.)

7.4 If Z₁, Z₂,…, Z₆ denotes a random sample from the standard normal distribution, find a number b such that

$P\left({\displaystyle \underset{i=1}{\overset{6}{\sum }}{Z}_i^2\le b}\right)=.95$.