The expected value of x is the sum of the product of each possible outcome and the probability of the outcome occurring. reacall,
probability = number of favourable outcomes/total number of outcomes
Looking at the table,
the total number of people is
4 + 3 + 4 + 4 + 2 + 3 = 20
The probability of choosing a person that is 3 years is 4/20 = 1/5
The probability of choosing a person that is 28 years is = 3/20
The probability of choosing a person that is 38 years is = 4/20 = 1/5
The probability of choosing a person that is 52 years is = 4/20 = 1/5
The probability of choosing a person that is 61 years is = 2/20 = 1/10
The probability of choosing a person that is 83 years is = 3/20
Thus, the expected value of x would be
4 * 1/5 + 3 * 3/20 + 4 * 1/5 + 4 * 1/5 + 2 * 1/10 + 3 * 3/20
= 0.8 + 0.45 + 0.8 + 0.8 + 0.2 + 0.45
= 3.5
The expected value of x is 3.5