Question

Christine ran a video game competition and recorded the scores of all the contestants. Score Number of people 426 4 572 1 859 2 900 1 1 951 2 X is the score that a randomly chosen person scored. What is the expected value of X? Write your answer as a decimal.

Answer 1

The expected value is defined by

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

We have to multiply each score by its probability

$\begin{gathered} E=426\cdot\frac{4}{10}+572\cdot\frac{1}{10}+859\cdot\frac{2}{10}+900\cdot\frac{1}{10}+951\cdot\frac{2}{10} \\ E=170.4+57.2+171.8+90+190.2 \\ E=679.6 \end{gathered}$

Hence, the expected value is 679.6.