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1 Probability calculations (a) A manufactured product consists of several different components that are fitted onto a base chassis. As the dimensions of each component can vary slightly, it sometimes happens that one or more components cannot be fitted in place and the partially assembled product must be sent to another section for extra fitting work. Investigations have shown that most of the fitting problems come from two particular components (identified as B and F): more precisely, the chance that a randomly chosen component of type B will not fit is 3.7% and the chance that a randomly chosen component of type F will not fit is 2.8%. i) Assuming that problems with fitting of these two components are independent of each other and that the components being assembled onto each base chassis are chosen randomly, what is the probability that there will be problems fitting both component. B and component.

1 Probability calculations (a) A manufactured product consists of several different components that are fitted onto a base chassis. As the dimensions of each component can vary slightly, it sometimes happens that one or more components cannot be fitted in place and the partially assembled product must be sent to another section for extra fitting work. Investigations have shown that most of the fitting problems come from two particular components (identified as B and F): more precisely, the chance that a randomly chosen component of type B will not fit is 3.7% and the chance that a randomly chosen component of type F will not fit is 2.8%. i) Assuming that problems with fitting of these two components are independent of each other and that the components being assembled onto each base chassis are chosen randomly, what is the probability that there will be problems fitting both component. B and component.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1 Probability calculations (a) A manufactured product consists of several different components that are fitted onto a base chassis. As the dimensions of each component can vary slightly, it sometimes happens that one or more components cannot be fitted in place and the partially assembled product must be sent to another section for extra fitting work. Investigations have shown that most of the fitting problems come from two particular components (identified as B and F): more precisely, the chance that a randomly chosen component of type B will not fit is 3.7% and the chance that a randomly chosen component of type F will not fit is 2.8%. i) (b) (c) Assuming that problems with fitting of these two components are independent of each other and that the components being assembled onto each base chassis are chosen randomly, what is the probability that there will be problems fitting both component B and component F on a given base chassis? ii) Under the same assumptions, what is the probability that there will be problems with fitting at least one of components B and F to a given base chassis? i) The number of customers visiting a specialty store each hour is denoted as N and has the following probability distribution: n 5 6 7 8 9 Pr(N = n) 0.1785 k 0.3105 0.1115 0.015 Find the value of k which makes this a valid distribution. ii) The time to failure T (in hours) of a certain mechanical component has a distribution with the probability density function (pdf): f(t) = 2.5 t-3.5 for t > 1. Find the mean E(T) of this variable. iii) In the scenario of part (ii), it can be shown that E(T2) = 5. Use this information to determine the variance Var (T) of the variable T. The failure ages of a particular electrical component are observed to follow an exponential distribution with an average failure rate of λ = 0.85 failures per year. Find the probability that a randomly chosen component fails between three and five years after being placed in service.
Transcribed Image Text:1 Probability calculations (a) A manufactured product consists of several different components that are fitted onto a base chassis. As the dimensions of each component can vary slightly, it sometimes happens that one or more components cannot be fitted in place and the partially assembled product must be sent to another section for extra fitting work. Investigations have shown that most of the fitting problems come from two particular components (identified as B and F): more precisely, the chance that a randomly chosen component of type B will not fit is 3.7% and the chance that a randomly chosen component of type F will not fit is 2.8%. i) (b) (c) Assuming that problems with fitting of these two components are independent of each other and that the components being assembled onto each base chassis are chosen randomly, what is the probability that there will be problems fitting both component B and component F on a given base chassis? ii) Under the same assumptions, what is the probability that there will be problems with fitting at least one of components B and F to a given base chassis? i) The number of customers visiting a specialty store each hour is denoted as N and has the following probability distribution: n 5 6 7 8 9 Pr(N = n) 0.1785 k 0.3105 0.1115 0.015 Find the value of k which makes this a valid distribution. ii) The time to failure T (in hours) of a certain mechanical component has a distribution with the probability density function (pdf): f(t) = 2.5 t-3.5 for t > 1. Find the mean E(T) of this variable. iii) In the scenario of part (ii), it can be shown that E(T2) = 5. Use this information to determine the variance Var (T) of the variable T. The failure ages of a particular electrical component are observed to follow an exponential distribution with an average failure rate of λ = 0.85 failures per year. Find the probability that a randomly chosen component fails between three and five years after being placed in service.
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