Chapter 6.1, Problem 7E

To determine

To Calculate: the mean and explain it

Answer to Problem 7E

  ${\mu }_x=\text{E}\left(X\right)=19.35$

Explanation of Solution

Given:

Money collected	0	5	10	15	20	25
Probability	0.02	0.05	0.08	0.16	0.27	0.42

Formula used:

  ${\mu }_x=\text{E}\left(X\right)={\displaystyle \sum {\text{P}}_i}{X}_i$

Calculation:

  $\begin{array}{l}{\mu }_x=\text{E}\left(X\right)={\displaystyle \sum {\text{P}}_i}{X}_i\\ {\mu }_x=\text{E}\left(X\right)=P_0{X}_0+P_1{X}_1+P_2{X}_2+P_3{X}_3+P_4{X}_4\\ =\left(0\right)\left(0.05\right)+\left(5\right)\left(0.05\right)+\left(10\right)\left(0.08\right)+\left(15\right)\left(0.16\right)+\left(20\right)\left(0.27\right)+\left(25\right)\left(0.42\right)\\ =0+0.25+0.8+2.4+5.4+10.5\\ =19.35\end{array}$

If many trips arbitrary choose, the average money will be collected $19.35. Maximum money collected which is $25 has the maximum probability and No money collected has the minimum probability.