Chapter 17, Problem 32E

To determine

To find: The airline is not going to have ample seats, so everyone is bumped.

Answer to Problem 32E

0.1497

Explanation of Solution

Given:

  $\begin{array}{c}n=275\\ p=0.95\end{array}$

Calculation:

The details surrounding the issue is that the possibilities are 0.05 for the passenger and 0.95 for the passenger and 275 for the overall number of tickets booked are.

There are fewer than 10 percent of passengers who do not show up

That is,

  $\begin{array}{c}np=13.75\\ nq=\left(275\right)\left(0.95\right)\\ =261.25\end{array}$

  $np\ge 10\text{ and }nq\ge \text{10}$

Binomial patterns can also be approximated to normal distribution.

Let X be number of passengers not displaying.

Standard deviation is,

  $\begin{array}{c}\sqrt{npq}=275\left(0.05\right)\left(0.95\right)\\ =3.614\end{array}$

Therefore, $X-N\left(13.75,3.614\right)$

The possibility must be identified that the airline does not have sufficient seats,

  $\begin{array}{c}P\left[X<10\right]=P\left[Z<\frac{10-13.75}{3.614}\right]\\ =P\left[Z<-1.038\right]\\ =0.1497\end{array}$