Question

ed ran a video game competition and recorded the scores of all the contestants. x is the score that a randomly chosen person scored. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Calculate the total number of people

$$4 + 2+1 + 1+1 + 1=10$$

Step2: Calculate the sum of (score × number of people)

$$238\times4+299\times2 + 391\times1+662\times1+949\times1+999\times1$$
$$=952+598+391+662+949+999$$
$$=952+598+(391+662)+(949+999)$$
$$=1550 + 1053+1948$$
$$=1550+(1053 + 1948)$$
$$=1550+3001$$
$$=4551$$

Step3: Calculate the expected value

The expected value formula is $E(X)=\frac{\sum_{i}(x_{i}\times n_{i})}{N}$, where $x_{i}$ is the score, $n_{i}$ is the number of people with that score, and $N$ is the total number of people.
So $E(X)=\frac{4551}{10}=455.1$

Answer:

$455.1$