Question

The members of the local garden club tallied the number of plants in each person's garden. Number of plants Number of gardens 16 2 26 5 76 3 X is the number of plants that a randomly chosen garden has. What is the expected value of X? Write your answer as a decimal.

Answer 1

First, we need to compute the probability associated to each x-value.

x = 16

P(16) = 2/(2 + 5 + 3) = 0.2

x = 26

P(26) = 5/(2 + 5 + 3) = 0.5

x = 76

P(76) = 3/(2 + 5 + 3) = 0.3

The expected value, E(x), is calculated as follows:

$\begin{gathered} E(x)=\sum ^{}_{}x\cdot P(x) \\ E(x)=16\cdot0.2+26\cdot0.5+76\cdot0.3 \\ E(x)=3.2+13+22.8 \\ E(x)=39 \end{gathered}$