Air America is considering a new policy of booking as many as 400 persons on an airplane that can sear only 350. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Estimate the probability that if Air America books 400 persons, not enough seats will be avaliable. Is that probability low enough to be workable, or should the policy be changed?
What are the chances that a person who is murdered actually knew the murderer? About 64% of people who are murdered actually knew the murderer. Suppose that a detective file in New Orleans has 63 unsolved murders. What is the probability that
A )at least 35 of the victims knew their murderers?
B) at most 48 of the victims knew their murderers?
c)less than 30 victims did not know their murderer?
d) More than 20 victims did not know their murderer?
To estimate the probability that there won't be enough seats available if Air America books 400 persons, we can follow these steps:
1. Calculate the number of expected passengers: Since past studies indicate that only 85% of booked passengers actually arrive for the flight, we can expect 85% of the booked 400 passengers, which is 0.85 * 400 = 340 passengers.
2. Calculate the probability of not enough seats: Since the airplane can seat only 350 persons, if the number of expected passengers (340) exceeds the seating capacity (350), there won't be enough seats available. So the probability can be calculated by subtracting the seating capacity from the expected passengers and dividing it by the total booked passengers (400). Thus, the probability is (400 - 350) / 400 = 50 / 400 = 0.125.
The calculated probability is 0.125 or 12.5%.
Now, whether this probability is low enough to be workable or not depends on Air America's specific needs and risk tolerance. Typically, airlines aim for much lower probabilities to ensure a comfortable experience for passengers and avoid overbooking situations. Therefore, in this case, the probability of not enough seats is relatively high, so the policy of booking 400 persons on a plane with a seating capacity of 350 may not be workable, and it might be advisable for Air America to consider changing this policy.