Assume that an airline operates a 10-seat Piper PA-31 on a particular route. Historically, the probability of a passenger showing up for a flight is 85%. 1. Assume that 10 tickets were sold. Let X be the number of passengers who showed up for the flight. a. Describe the distribution of X: X∼X∼ (n=(n= ,p=,p= )) b. Find the probability that the flight is not full, in other words, find the probability that not all passengers will show up: P(X≤P(X≤ )=)= (Round the answer to 4 decimal places) c. Find the expected number of passengers who show up for the flight: E[X]=E[X]= (Round the answer to the whole number) d. Find the expected number of empty seats by subtracting the E[X]E[X] from the plane capacity:
Assume that an airline operates a 10-seat Piper PA-31 on a particular route. Historically, the
1. Assume that 10 tickets were sold. Let X be the number of passengers who showed up for the flight.
a. Describe the distribution of X:
X∼X∼ (n=(n= ,p=,p= ))
b. Find the probability that the flight is not full, in other words, find the probability that not all passengers will show up:
P(X≤P(X≤ )=)= (Round the answer to 4 decimal places)
c. Find the expected number of passengers who show up for the flight:
E[X]=E[X]= (Round the answer to the whole number)
d. Find the expected number of empty seats by subtracting the E[X]E[X] from the plane capacity:
(Round the answer to the whole number)
2. Assume that the airline sells 1 more ticket(s). Let Y be the number of passengers who showed up for the flight.
a. Describe the distribution of Y:
Y∼Y∼ (n=(n= ,p=,p= ))
b. Find the probability that more passengers will show up than the plane can carry:
P(Y>P(Y> )=)= (Round the answer to 4 decimal places)
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