Question

At a candy factory, butterscotch candies were packaged into bags of different sizes. Number of butterscotch candies Number of bags 16 5 18 5 50 5 103 2 150 3 X is the number of butterscotch candies that a randomly chosen bag had. What is the expected val X? Write your answer as a decimal.

Answer 1

Determine the total number of butterscotch candies.

$\begin{gathered} T=16+18+50+103+150 \\ =337 \end{gathered}$

Determine the expected value of X.

$\begin{gathered} E(X)=\frac{16}{337}\cdot5+\frac{18}{337}\cdot5+\frac{50}{337}\cdot5+\frac{103}{337}\cdot2+\frac{150}{337}\cdot3 \\ =0.237+0.267+0.742+0.611+1.335 \\ =3.192 \end{gathered}$

Thus, expected value is 3.192.