A commercial jet aircraft has four engines. For an aircraft in flight to land safely, at least two engines should be in working condition. Each engine has an independent reliability of p 92%. a. What is the probability that an aircraft in flight can land safely? b. If the probability of landing safely must be at least 99.5%, what is the minimum value for p? Repeat the question for probability of landing safely to be 99.9%. c. 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. d. 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?
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.
A commercial jet aircraft has four engines. For an aircraft in flight to land
safely, at least two engines should be in working condition. Each engine has an independent reliability of p 92%.
a. What is the
b. If the probability of landing safely must be at least 99.5%, what is the minimum value for p? Repeat the question for probability of landing safely to
be 99.9%.
c. 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.
d. 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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