Concept explainers
a
Interpretation:
Probability of cab to run without breakdown
Concept Introduction:
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
a
Answer to Problem 51AP
Probability of cab to run without breakdown is 0.1353.
Explanation of Solution
Given information:
Number of cabs = 10
Number of cabs breakdown = 2
The probability that any particular cab will run for a full year without suffering a breakdown is as follows:
Time period (t) = 1 year
Therefore,
b
Interpretation:
Probability that entire fleet will run without breakdown a month.
Concept Introduction:
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
b
Answer to Problem 51AP
Probability that entire fleet will run without breakdown a month is 0.1889.
Explanation of Solution
Given information:
Number of cabs = 10
Number of cabs breakdown = 2
The probability that the entire fleet will run for one month without a breakdown is as follows:
Time period (t) = 1/12 year
Calculate the probability that there is no breakdown in one month as shown below:
c
Interpretation:
Number of breakdown in 3 months period time.
Concept Introduction:
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
c
Answer to Problem 51AP
Number of breakdown in 3 months period time is 5.
Explanation of Solution
Given information:
Number of cabs = 10
Number of cabs breakdown = 2
The average no. of breakdowns that are expected in the typical three month period is as follows:
The number of breakdowns expected for the entire fleet is calculated below:
Expected no. of breakdown = Total no. of cars
d
Interpretation:
Probability of more than 5 breakdown from Thanksgiving day and New year’s day
Concept Introduction:
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
d
Answer to Problem 51AP
Probability of more than 5 breakdown from Thanksgiving day and New year’s day is 0.
Explanation of Solution
Given information:
Number of cabs = 10
Number of cabs breakdown = 2
Formula to calculate the required probability is shown below:
The probability that there are more than five breakdowns between Nov 28 and Jan 1 (35days) of the same year is depending on the Poisson process with
e
Interpretation:
Reason for low value in part (d)
Concept Introduction:
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
e
Explanation of Solution
The given period between Thanksgiving Day and New Year’s Eve is expected to be busier as compared to normal time period. Therefore, the probability for more than 5 breakdowns would be low during the period.
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Chapter 13 Solutions
Production and Operations Analysis, Seventh Edition
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