Use a table to find or estimate ${\chi }^2$ such that:
$P(X^2>{\chi }^2)=0.010$ (Area to the right)
$df=50$

• A. 27.99
• B. 29.71
• C. 76.15
• D. 79.49

Answer: (C)

Verified step by step guidance

1. Identify the distribution involved: here, it is the chi-square distribution with degrees of freedom (df) equal to 50.
2. Understand the problem: you need to find the chi-square value \( \chi^2 \) such that the probability that the chi-square random variable \( X^2 \) exceeds this value is 0.010, i.e., \( P(X^2 > \chi^2) = 0.010 \). This means you are looking for the 99th percentile (or the upper 1% point) of the chi-square distribution with 50 degrees of freedom.
3. Use a chi-square distribution table or statistical software: locate the row corresponding to \( df = 50 \), then find the column corresponding to the upper tail probability of 0.010 (right-tail area = 0.010).
4. Read off or interpolate the value of \( \chi^2 \) from the table that matches the given probability and degrees of freedom. If the exact value is not listed, use interpolation between the closest values.
5. This value you find is the critical chi-square value such that the area to the right under the chi-square curve with 50 degrees of freedom is 0.010.