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)=(16)/(337)\cdot5+(18)/(337)\cdot5+(50)/(337)\cdot5+(103)/(337)\cdot2+(150)/(337)\cdot3 \\ =0.237+0.267+0.742+0.611+1.335 \\ =3.192 \end{gathered}`

Thus, expected value is 3.192.