Question

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, 25% 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.)

(a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

(b) If six reservations are made, what is the expected number of available places when the limousine departs?

(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 0.09 0.25 0.29 0.37 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

Answer #1

a)

P(arrival of a random person) =p= | 0.75 | |||||

P(at
least one can't)=1-P(at most 4 will
appear)=1-∑_{x=0}^{4 }
(_{6}C_{x})p^{x}(1−p)^{(6-x)}
= |
0.5339 |

b)

expected available spaces =E(4-x) = |
∑_{x=0}^{4}
(4-x)*(_{6}C_{x})p^{x}(1-p)^{6-x}= |
0.2119 |

c)

let y be the number of reservations made: | ||||||

probability mass function of X: =P(X=x)=Σ_{y=3}^{6}
P(Y=y)*P(X=x|y)=Σ_{y=3}^{6}
P(y)*(_{y}C_{x})*p^{x}(1-p)^{y-x} |

x |
0 |
1 |
2 |
3 |
4 |

P(x) |
0.0028 |
0.0302 |
0.1284 |
0.2687 |
0.5699 |

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, 15% 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.)
(a) If six reservations are made, what is the probability that
at least one individual with a reservation...

An airport limousine ca 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 20% of all those making reservations do not appear for the
trip. Answer the following questions, assuming independence
wherever appropriate
a) If six reservations are made, what is the probability that at
least one individual with a reservation cannot be accommodated on
the trip?
b)...

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, 30% 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.)
Suppose the probability distribution of the number of
reservations made is given in the accompanying table.
Number of...

An airport limousine can accommodate up to 4 passengers on any
one trip. The company will accept a maximum of 6 reservations for a
trip, and a passenger must have a reservation. From previous
records, 20% of all those making reservations do not show up for
the trip. Answer the following questions assuming independence
wherever appropriate.
A) Assume that six reservations are made. Let X = the number of
customers who have made a reservation and show up for the...

An airport limousine service (something like Super Shuttle) can
accommodate up to 4 passengers on any one trip. A passenger must
make an advanced reservation to make a trip (no walk-ups) and
accepts a maximum of six reservations for a trip, knowing that 20%
of all persons making reservations do not appear for the trip. The
probability distribution for the number of reservations made is
below:
Number of Reservations 3 4 5 6
Probability 0.1 0.2 0.3 0.4
Each passenger...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 10 minutes ago

asked 22 minutes ago

asked 27 minutes ago

asked 41 minutes ago

asked 49 minutes ago

asked 49 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago