374,799 views
32 votes
32 votes
At their family reunion, the Meyer family recorded everyone's age. Age Tabeople 3 4 28 3. 38 4 52 4 61 2 83 3 X is the age of a randomly chosen person. What is the expected value of x? Write your answer as a decimal.

User Moona
by
3.5k points

1 Answer

23 votes
23 votes

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

User Kurikintoki
by
2.9k points