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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.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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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)
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