Question

Dave counted the number of peanuts in each bag of trail mix. Number of peanuts Number of bags 51 1 74 6 107 3 X is the number of peanuts that a randomly chosen bag had. What is the expected value of X? Write your answer as a decimal.

Answer 1

The expected value formula is

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

We have to multiply each value by its probability and sum them all

$\begin{gathered} E=51\cdot\frac{1}{10}+74\cdot\frac{6}{10}+107\cdot\frac{3}{10} \\ E=5.1+44.4+32.1 \\ E=81.6 \end{gathered}$

Hence, the expected value is 81.6.