The Following Table Shows the Approximate Numbers of School Goers

Multiple Choice

The following table shows the approximate numbers of school goers in the U.S. (residents who attended some educational institution) in 1998, broken down by age group. Use the rounded midpoints of the given measurement classes to compute the probability distribution of the age X of a school goer. (Round probabilities to two decimal places.) Hence compute the expected value of X. $$\begin{array} { c c c c c c c } \text { Age } & 3 - 6.9 & 7 - 12.9 & 13 - 16.9 & 17 - 22.9 & 23 - 26.9 & 27 - 42.9 \\\begin{array} { c } \text { Population } \\\text { (Millions) }\end{array} & 11 & 22 & 16 & 15 & 4 & 7\end{array}$$

A) $E ( X ) = 15.2$
B) $E ( X ) = 0.99$
C) $E ( X ) = 7.65$
D) $E ( X ) = 12.05$
E) $E ( X ) = 10.8$