Question

30 POINTS! HELP!!
The table shows the probability distribution of siblings of students in a high school with 1500 students. What is the expected value for the number of siblings of a randomly chosen student?
A. 2.5
B. 1.29
C. 1.08
D. 1.11

Answer 1

Answer is 1.08, i believe this might be an estimated number, with the way I did it

Answer 2

The expected value for the number of siblings of a randomly chosen student is 1.11.

What is expected value mean?

"In a probability distribution, the weighted average of possible values of a random variable, with weights given by their respective theoretical probabilities, is known as the expected value".

For the given situation,

The table shows the probability distribution of siblings of students in a high school with 1500 students.

For number of siblings = 0, Probability = 0.18.

For number of siblings = 1, Probability = 0.65.

For number of siblings = 2, Probability = 0.09.

For number of siblings = 3, Probability = 0.05.

For number of siblings = 4, Probability = 0.02.

For number of siblings = 5, Probability = 0.01.

The formula for expected value mean, E(x) = ΣxP(x)

$E(x)=(0)(0.18)+(1)(0.65)+(2)(0.09)+(3)(0.05)+(4)(0.02)+(5)(0.01)$

⇒ $E(x)=1.11$

Hence we can conclude that the expected value for the number of siblings of a randomly chosen student is 1.11.

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