Question

An airline company is considering a new policy of booking as many as 318 persons on an airplane that can seat only 310. (Past studies have revealed that only 90% of the booked passengers actually arrive for the flight.) Estimate the probability that if the company books 318 persons. not enough seats will be available.

Answer 1

Answer:

Hence, the required probability is $0.0004$.

Given :

$90\%$ of the booked passengers arrive for the flight.

Number of booked passengers n $=318$

Number of seats available x $=310$

To find :

The probability that if the company books 318 persons.

Explanation :

$n=318,x=310$

$P=0.09(90\%)$

Mean  $\bar{x}=nP$

   $\Rightarrow \bar{x}=318\times 0.09$

  $\Rightarrow \bar{x}=28.62$

Standard deviation $\sigma =\sqrt{nPq$    where $q=1-P$

         $\Rightarrow \sigma =\sqrt{318\times 0.09\times 0.91}$

        $\Rightarrow \sigma=\sqrt{26.0442}$

        $\Rightarrow \sigma =5.1033$

Required probability$=P(x>310)$

                                 $=1-P(x$

                                $=1-P(\frac{x-\bar{x}}{\sigma}$

                               $=1-P(z$

                              $=1-0.9995$

                               $=0.0004$