In: Statistics and Probability
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 35% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)
(b) If six reservations are made, what is the expected number of
available places when the limousine departs?
places
(c) Suppose the probability distribution of the number of
reservations made is given in the accompanying table.
Number of reservations | 3 | 4 | 5 | 6 |
Probability | 0.15 | 0.22 | 0.35 | 0.28 |
Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.
x | 0 | 1 | 2 | 3 | 4 |
p(x) |