A rental car company will have 100 cars available for rent on a particular day. It expects that demand for that day will be very high, so demand is certain to be higher than 300 bookings. If it expects a 15% no-show rate, what booking level should it set if it wants to ensure that the probability that a booking will be denied service is 0.0002? (You can use the normal approximation to the binomial distribution, as described below, to estimate your answer.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
icon
Related questions
Topic Video
Question
100%

A rental car company will have 100 cars available for rent on a particular day. It expects that
demand for that day will be very high, so demand is certain to be higher than 300 bookings. If
it expects a 15% no-show rate, what booking level should it set if it wants to ensure that the
probability that a booking will be denied service is 0.0002? (You can use the normal
approximation to the binomial distribution, as described below, to estimate your answer.)

4. A rental car company will have 100 cars available for rent on a particular day. It expects that
demand for that day will be very high, so demand is certain to be higher than 300 bookings. If
it expects a 15% no-show rate, what booking level should it set if it wants to ensure that the
probability that a booking will be denied service is 0.0002? (You can use the normal
approximation to the binomial distribution, as described below, to estimate your answer.)
The p.d.f. for the binomial distribution is
for x = 0, 1, ... , n
(В.7)
where
)-
n!
(n – x)!x!
The mean of the binomial distribution is pn, the variance is p(1 – p)n, and the standard
deviation is Vp(1 – p)n.
Because of the terms of the form in Equation B.7, the binomial distribution can be very
difficult to work with in practice. In particular, there is no easy way to calculate the c.d.f.
F(x) for a binomial distribution. Fortunately, for large n, the binomial distribution is
well approximated by the normal distribution with mean u = pn and standard deviation
o = Vpqn. This approximation is quite useful; however, it is subject to some of the same
cautions as the use of the discrete normal distribution.
Transcribed Image Text:4. A rental car company will have 100 cars available for rent on a particular day. It expects that demand for that day will be very high, so demand is certain to be higher than 300 bookings. If it expects a 15% no-show rate, what booking level should it set if it wants to ensure that the probability that a booking will be denied service is 0.0002? (You can use the normal approximation to the binomial distribution, as described below, to estimate your answer.) The p.d.f. for the binomial distribution is for x = 0, 1, ... , n (В.7) where )- n! (n – x)!x! The mean of the binomial distribution is pn, the variance is p(1 – p)n, and the standard deviation is Vp(1 – p)n. Because of the terms of the form in Equation B.7, the binomial distribution can be very difficult to work with in practice. In particular, there is no easy way to calculate the c.d.f. F(x) for a binomial distribution. Fortunately, for large n, the binomial distribution is well approximated by the normal distribution with mean u = pn and standard deviation o = Vpqn. This approximation is quite useful; however, it is subject to some of the same cautions as the use of the discrete normal distribution.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,