9:17 PM Wed Feb 26 \( 26 \% \) Emilio Mejia F... PP. 5 Expected values of random va... Video 49:09 For a math assignment, Lila researched the scores of the people competing on her favorite quiz show. Quiz show scores \[ \begin{array}{llllllllll} 766 & 766 & 766 & 804 & 804 & 804 & 883 & 883 & 883 & 951 \end{array} \] \( X \) is the score that a randomly chosen person scored. What is the expected value of \( X \) ? Write your answer as a decimal. \( \square \) Submit Next up

To calculate the expected value of the quiz show scores, you'll want to take a weighted average of the scores based on their frequency. First, count how many times each score appears: 766 appears three times, 804 three times, 883 three times, and 951 once. Then, sum the products of each score and its frequency: \[ E(X) = \frac{(766 \times 3) + (804 \times 3) + (883 \times 3) + (951 \times 1)}{3 + 3 + 3 + 1} \] Calculate that to find the expected value! Don’t forget, using expected value is like seeing into the future—it gives you a snapshot of what to expect based on past data. It's a valuable tool in statistics, often helping with decisions in economics, finance, and game design! Knowing the expected value helps understand what outcomes are most likely and aids in strategic planning.