**16. Correct. The
answer is true**

(a) If the area to the right of χ^{
2}_{2} = 0.05, then the area to the left of χ^{ }_{2}
= 0.95 and χ^{2}_{2} represents the 95^{th}
percentile, χ_{0.95}^{2}. From the table on chi-squared
distribution, it follows that χ^{2}_{2}=11.1.

(b) Since the distribution is not
symmetric, there are many values for which the total area to the left of χ^{2}_{1}
and to the right of χ^{2}_{2} = 0.05. For example, the
area to the left of χ^{2}_{1} could be 0.03 and to the
right of χ^{2}_{2} could be 0.02. However, it is customary
to choose the two areas equal. In this case each area = 0.025. If the area to
the right of χ^{2}_{2 }is 0.025, then the area to its left
is 0.975 and χ^{2}_{2} represents the 97.5^{th}
percentile, which according to the Chi-Square distribution table is 12.8. Similarly, if the area to the left of χ^{2}_{1
}is 0.025, then χ^{2}_{1} represents the 2.5^{th}
percentile which according to the Chi-Square distribution table is 0.831.

(c) If the area to the left of χ^{
2}_{1} is 0.10, then χ^{ 2}_{1} represents
the 10^{th} percentile, which equals 1.61.

(d) If the area to the right of χ^{2}_{2}
is 0.01, then χ^{2}_{2} represents the 99^{th}
percentile which equals 15.1