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 find the expected value of the score \( X \) of a randomly chosen person, we need to calculate the average of all the scores provided. Given scores: \[ 766, 766, 766, 804, 804, 804, 883, 883, 883, 951 \] To find the expected value, we sum up all the scores and divide by the total number of scores. Expected value \( E(X) = \frac{\text{Sum of all scores}}{\text{Total number of scores}} \) Let's calculate the expected value: Calculate the value by following steps: - step0: Calculate: \(\frac{\left(766+766+766+804+804+804+883+883+883+951\right)}{10}\) - step1: Remove the parentheses: \(\frac{766+766+766+804+804+804+883+883+883+951}{10}\) - step2: Write as a multiplication: \(\frac{766\times 3+804\times 3+883\times 3+951}{10}\) - step3: Multiply the numbers: \(\frac{2298+804\times 3+883\times 3+951}{10}\) - step4: Multiply the numbers: \(\frac{2298+2412+883\times 3+951}{10}\) - step5: Multiply the numbers: \(\frac{2298+2412+2649+951}{10}\) - step6: Add the numbers: \(\frac{8310}{10}\) - step7: Reduce the numbers: \(\frac{831}{1}\) - step8: Calculate: \(831\) The expected value of the score \( X \) is 831.