3–41. A commercial jet aircraft has four engines. For an aircraft in flflight to land safely, at least two engines should be in working condition. Each engine has an inde pendent reliability of p 92%. What is the probability that an aircraft in flflight can land safely? If the probability of landing safely must be at least 99.5%, what is the mini mum value for p? Repeat the question for probability of landing safely to be 99.9%. If the reliability cannot be improved beyond 92% but the number of engines in a plane can be increased, what is the minimum number of engines that would achieve at least 99.5% probability of landing safely? Repeat for 99.9% probability. One would certainly desire 99.9% probability of landing safely. Looking at the answers to (b) and (c), what would you say is a better approach to safety, increasing the number of engines or increasing the reliability of each engine?
3–41. A commercial jet aircraft has four engines. For an aircraft in flflight to land safely, at least two engines should be in working condition. Each engine has an inde pendent reliability of p 92%. What is the probability that an aircraft in flflight can land safely? If the probability of landing safely must be at least 99.5%, what is the mini mum value for p? Repeat the question for probability of landing safely to be 99.9%. If the reliability cannot be improved beyond 92% but the number of engines in a plane can be increased, what is the minimum number of engines that would achieve at least 99.5% probability of landing safely? Repeat for 99.9% probability. One would certainly desire 99.9% probability of landing safely. Looking at the answers to (b) and (c), what would you say is a better approach to safety, increasing the number of engines or increasing the reliability of each engine?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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3–41. A commercial jet aircraft has four engines. For an aircraft in flflight to land
safely, at least two engines should be in working condition. Each engine has an inde
pendent reliability of p 92%.
- What is the
probability that an aircraft in flflight can land safely? - If the probability of landing safely must be at least 99.5%, what is the mini
mum value for p? Repeat the question for probability of landing safely to
be 99.9%.
- If the reliability cannot be improved beyond 92% but the number of
engines in a plane can be increased, what is the minimum number of
engines that would achieve at least 99.5% probability of landing safely?
Repeat for 99.9% probability.
- One would certainly desire 99.9% probability of landing safely. Looking
at the answers to (b) and (c), what would you say is a better approach
to safety, increasing the number of engines or increasing the reliability of
each engine?
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