Find the expected value.
-The following table gives the distribution of heights for female students at one U.S. college. $$\begin{array}{l}
\text { Height category }\
\begin{array} { l | l }
\text { (inches) } & \text { Percentage } \
\hline 57 - 59 & 7.2 \
60 - 62 & 20.5 \
63 - 65 & 36.9 \
66 - 68 & 19.7 \
69 - 71 & 10.5 \
72 \text { and over } & 5.2
\end{array}
\end{array}$$ Find the expected value of height for women at this college. Use the midpoint of each category, (for example use 58 for the 57-59 category). Use 74 for the 72 and over category.

Question

Find the expected value.
-The following table gives the distribution of heights for female students at one U.S. college. $$\begin{array}{l}
\text { Height category }\
\begin{array} { l | l } 
\text { (inches) } & \text { Percentage } \
\hline 57 - 59 & 7.2 \
60 - 62 & 20.5 \
63 - 65 & 36.9 \
66 - 68 & 19.7 \
69 - 71 & 10.5 \
72 \text { and over } & 5.2
\end{array}
\end{array}$$ Find the expected value of height for women at this college. Use the midpoint of each category, (for example use 58 for the 57-59 category). Use 74 for the 72 and over category.

Quizplus · Accepted Answer

To find the expected value of height, we calculate the weighted average using the midpoint of each category and the corresponding percentage. The calculation is as follows:- For 57-59 inches, the midpoint is 58 inches. The expected value contribution is $58 \times 0.072 = 4.176$.- For 60-62 inches, the midpoint is 61 inches. The expected value contribution is $61 \times 0.205 = 12.505$.- For 63-65 inches, the midpoint is 64 inches. The expected value contribution is $64 \times 0.369 = 23.616$.- For 66-68 inches, the midpoint is 67 inches. The expected value contribution is $67 \times 0.197 = 13.199$.- For 69-71 inches, the midpoint is 70 inches. The expected value contribution is $70 \times 0.105 = 7.35$.- For 72 and over, we use 74 inches as the midpoint. The expected value contribution is $74 \times 0.052 = 3.848$.Adding these contributions together gives the expected value of height:$$4.176 + 12.505 + 23.616 + 13.199 + 7.35 + 3.848 = 64.694$$Rounded to one decimal place, the expected value is 64.7 inches.

Find the Expected Value Find the Expected Value of Height for Women at This