The time (in hours) to failure of a component is exponential distributed with mean 40. In a manufacturing process, the machine involved uses one of these components continuously until it fails. a) Find the probability that a component will fail during a 12 to 18 hours shift. b) A component has not failed for 30 hours. Find the probability that this component lasts for at least another 30 hours.

The time (in hours) to failure of a component is exponential distributed with mean 40. In a manufacturing process, the machine involved uses one of these components continuously until it fails. a) Find the probability that a component will fail during a 12 to 18 hours shift. b) A component has not failed for 30 hours. Find the probability that this component lasts for at least another 30 hours.

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Description: The time (in hours) to failure of a component is exponential distributed with mean 40. In amanufacturing process, the machine involved uses one of these components continuously until itfails.a) Find the probability that a component will fail during

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

The time (in hours) to failure of a component is exponential distributed with mean 40. In a
manufacturing process, the machine involved uses one of these components continuously until it
fails.
a) Find the probability that a component will fail during a 12 to 18 hours shift.
b) A component has not failed for 30 hours. Find the probability that this component lasts for at
least another 30 hours.

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