An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0.90. If the airline sells 105 tickets, what is the probability that everyone who appears for the flight will get a seat?
Step1 of 3:
We have An airplane and it has 100 seats of passengers.
Assume that the P( a person holding a ticket appears for the flight) = 0.90.
That is x = 100 p = 0.90.
We need to the probability that everyone who appears for the flight will get a seat when the airline sells 105 tickets.
Step2 of 3:
Here X be the random variable it represents the number of people out of 105 who appear for the flight. That is n = 105.
Let X follows binomial distribution with parameters “n and p ”.
Then the probability mass function of binomial distribution is given by:
, x = 0,1,2,...,n.
n = sample size
x = random variable
p = probability of success
q = 1 - p (probability of failure)
= 1 - 0.90
1).Mean of the binomial distribution is
Hence, = 94.5.
2).Standard deviation of binomial distribution is