Assume that an airline operates a 162-seat Boeing 757 on a particular route. Historically, the probability of a passenger showing up for a flight is 94%.

1. Assume that 162 tickets were sold. Let X be the number of passengers who showed up for the flight.

a. Describe the distribution of X:

 $\displaystyle {X}∼$? F Z B T N $\displaystyle {\left({n}=\right.}$ $\displaystyle ,{p}=$ $\displaystyle {)}$ 

b. Find the probability that the flight is not full, in other words, find the probability that not all passengers will show up:

$\displaystyle {P}{\left({X}\leq\right.}$ $\displaystyle {)}=$  (Round the answer to 4 decimal places)

c. Find the expected number of passengers who show up for the flight:

$\displaystyle {E}{\left[{X}\right]}=$  (Round the answer to the whole number)

d. Find the expected number of empty seats by subtracting the $\displaystyle {E}{\left[{X}\right]}$  from the plane capacity:

(Round the answer to the whole number)

2. Assume that the airline sells 5 more ticket(s). Let Y be the number of passengers who showed up for the flight.

a. Describe the distribution of Y:

 $\displaystyle {Y}∼$? B Z T F N $\displaystyle {\left({n}=\right.}$ $\displaystyle ,{p}=$ $\displaystyle {)}$ 

b. Find the probability that more passengers will show up than the plane can carry:

 $\displaystyle {P}{\left({Y}>\right.}$ $\displaystyle {)}=$ (Round the answer to 4 decimal places)$\displaystyle$