Chapter 5.3, Problem 109AYU

(a)

To determine

To find:The probability that $x=15$ the cars will arrive between $5:00\text{PM}$ and $6:00\text{PM}$ .

Explanation of Solution

The probability that $x$ cars will arrive between $5:00\text{PM}$ and $6:00\text{PM}$ is given by,

  $P\left(x\right)=\frac{{20}^x{e}^{-20}}{x!}$

Substitute $15$ for $x$ in the above expression.

  $\begin{array}{c}P\left(15\right)=\frac{{20}^{15}{e}^{-20}}{15!}\\ =0.0516\\ \approx 0.05\end{array}$

Therefore, The probability that $x=15$ the cars will arrive between $5:00\text{PM}$ and $6:00\text{PM}$ is $0.05$ .

(b)

To determine

To find:The probability that $x=20$ the cars will arrive between $5:00\text{PM}$ and $6:00\text{PM}$ .

Explanation of Solution

The probability that $x$ cars will arrive between $5:00\text{PM}$ and $6:00\text{PM}$ is given by,

  $P\left(x\right)=\frac{{20}^x{e}^{-20}}{x!}$

Substitute $20$ for $x$ in the above expression.

  $\begin{array}{c}P\left(1\right)=\frac{{20}^{20}{e}^{-20}}{20!}\\ =0.0888\\ \approx 0.09\end{array}$

Therefore, The probability that $x=20$ the cars will arrive between $5:00\text{PM}$ and $6:00\text{PM}$ is $0.09$ .