Homework Help is Here – Start Your Trial Now!
Math
Statistics
A long-distance taxi service company owns three vehicles. These vehicles are of different ages and have different repair records. The probabilities that, on any given day, each vehicle will be available for use are 0.90, 0.80, and 0.85. Whether one vehicle is available is independent of whether any other vehicle is available. a) Find the probability distribution for the number of vehicles available for use on a given day. (Hint: define a random variable X as the number of vehicles available for use on a given day. Now, figure out how many different values it can assume and what are the corresponding probabilities?) b) Find the expected number of vehicles available for use on a given day. c) Find the standard deviation of the number of vehicles available for use on a given day.

A long-distance taxi service company owns three vehicles. These vehicles are of different ages and have different repair records. The probabilities that, on any given day, each vehicle will be available for use are 0.90, 0.80, and 0.85. Whether one vehicle is available is independent of whether any other vehicle is available. a) Find the probability distribution for the number of vehicles available for use on a given day. (Hint: define a random variable X as the number of vehicles available for use on a given day. Now, figure out how many different values it can assume and what are the corresponding probabilities?) b) Find the expected number of vehicles available for use on a given day. c) Find the standard deviation of the number of vehicles available for use on a given day.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
Show full answers and steps to part a) b) & c)
A long-distance taxi service company owns three vehicles. These vehicles are of different ages and have different repair records. The probabilities that, on any given day, each vehicle will be available for use are 0.90, 0.80, and 0.85. Whether one vehicle is available is independent of whether any other vehicle is available. a) Find the probability distribution for the number of vehicles available for use on a given day. (Hint: define a random variable X as the number of vehicles available for use on a given day. Now, figure out how many different values it can assume and what are the corresponding probabilities?) b) Find the expected number of vehicles available for use on a given day. c) Find the standard deviation of the number of vehicles available for use on a given day. d) Suppose that you observe this taxi company for a month (30 days) and you are particularly interested in the number of days that the company has all three vehicles available in a month. i. Discuss under which assumption(s) the binomial model would be a good fit to answer this question. ii. What is the probability distribution of the number of days that the com- pany has all three vehicles available in a month? iii. What is the probability that there will be exactly 8 days that the company has all three vehicles available in a month? (You don't need to do the calculations, it is enough to give the expression that gives the desired probability)
Transcribed Image Text:A long-distance taxi service company owns three vehicles. These vehicles are of different ages and have different repair records. The probabilities that, on any given day, each vehicle will be available for use are 0.90, 0.80, and 0.85. Whether one vehicle is available is independent of whether any other vehicle is available. a) Find the probability distribution for the number of vehicles available for use on a given day. (Hint: define a random variable X as the number of vehicles available for use on a given day. Now, figure out how many different values it can assume and what are the corresponding probabilities?) b) Find the expected number of vehicles available for use on a given day. c) Find the standard deviation of the number of vehicles available for use on a given day. d) Suppose that you observe this taxi company for a month (30 days) and you are particularly interested in the number of days that the company has all three vehicles available in a month. i. Discuss under which assumption(s) the binomial model would be a good fit to answer this question. ii. What is the probability distribution of the number of days that the com- pany has all three vehicles available in a month? iii. What is the probability that there will be exactly 8 days that the company has all three vehicles available in a month? (You don't need to do the calculations, it is enough to give the expression that gives the desired probability)
Expert Solution
steps

Step by step

Solved in 4 steps with 22 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS