Chapter 14, Problem 1E

To determine

Find the number of expected oranges.

Answer to Problem 1E

The number of expected oranges is 33.

Explanation of Solution

Calculation:

The number of oranges per three and the distribution is given.

Expected value:

If X is a discrete random variable with the probability $P\left(x\right)$ , then the expected value of X is defined as, $\mu =E\left(X\right)={\displaystyle \sum _{x}x\times P\left(x\right)}$ .

The expected number of oranges:

$\begin{array}{c}\mu =E\left(\text{Oranges}\right)\\ ={\displaystyle \sum _{x=25}^{40}xP\left(x\right)}\\ =25\times 0.10+30\times 0.40+35\times 0.30+40\times 0.20\\ =2.5+12+10.5+8\\ =33\end{array}$

Hence, the number of expected oranges is 33.