An Airliner has a capacity for 300 passengers. If the company overbook a flight with 320 passengers, What is the probability that it will not be enough seats to accommodate all passengers. Assume that the probability that a randomly selected passenger shows up to the airport is 0.96. Find the probability using the normal distribution as an approximation to the binomial distribution.

The probability is  

Step-by-step explanation:

From the question we are told that

 The capacity of  an Airliner  is  k =  300 passengers

 The sample size n =  320 passengers

  The probability the a randomly selected passenger shows up on to the airport

Generally the mean is mathematically represented as

  =>

    =>

Generally the standard deviation is  

=>  

=>

Applying Normal approximation of binomial distribution

Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as

Here

=>

Now applying  continuity correction we have

=>    

=>    

From the z-table  

So