Question

While hanging Christmas lights for neighbors, Terrell counted the number of broken lights on each string Number of broken lights Number of strings 10 3 42 4 93 6 101 4 135 3 < is the number of broken lights that a randomly chosen string had. What is the expected value of X? Vrite your answer as a decimal.

Answer 1

The expected value is defined by

`E=\Sigma x\cdot P(x)`

This means we have to find the probability of each number of broken lights:

`\begin{gathered} P_1=(3)/(20) \\ P_2=(4)/(20)=(1)/(5) \\ P_3=(6)/(20)=(3)/(10) \\ P_4=(4)/(20)=(1)/(5) \\ P_5=(3)/(20) \end{gathered}`

Then, we multiply each probability by its x-value, and we add them to find the expected value:

`\begin{gathered} E=10\cdot(3)/(20)+42\cdot(1)/(5)+93\cdot(3)/(10)+101\cdot(1)/(5)+135\cdot(3)/(20) \\ E=1.5+8.4+27.9+20.2+20.25 \\ E=78.25 \end{gathered}`

Hence, the expected value is 78.25.