Answer:
The probability is 0.0144
Step-by-step explanation:
The probability that x people show up follows a binomial distribution, so it is equal to:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]
Where n is the number of booked people and p is the probability that a person shows up. Then, the probability that x people show up is:
[tex]P(x)=\frac{75!}{x!(75-x)!}*0.92^{x}*(1-0.92)^{75-x}[/tex]
So, the probability that the number of people who show up will exceed the capacity of the plane is:
P(x>73) = P(74) + P(75)
Where P(74) and P(75) are calculated as:
[tex]P(74)=\frac{75!}{74!(75-74)!}*0.92^{74}*(1-0.92)^{75-74}=0.0125[/tex]
[tex]P(75)=\frac{75!}{75!(75-75)!}*0.92^{75}*(1-0.92)^{75-75}=0.0019[/tex]
Finally, P(x>73) is:
P(x>73) = 0.0125 + 0.0019 = 0.0144
