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The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor
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Aircraft engines Engineers define reliability as the probability that an item will

Chapter 6, Problem 86

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QUESTION:

Aircraft engines Engineers define reliability as the probability that an item will perform its function under specific conditions for a specific period of time. A certain model of aircraft engine is designed so that each engine has probability 0.999 of performing properly for an hour of flight. Company engineers test an SRS of 350 engines of this model. Let X = the number that operate for an hour without failure. (a) Explain why X is a binomial random variable. (b) Find the mean and standard deviation of X. Interpret each value in context. (c) Two engines failed the test. Are you convinced that this model of engine is less reliable than its supposed to be? Compute P(X 348) and use the result to justify your answer.

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QUESTION:

Aircraft engines Engineers define reliability as the probability that an item will perform its function under specific conditions for a specific period of time. A certain model of aircraft engine is designed so that each engine has probability 0.999 of performing properly for an hour of flight. Company engineers test an SRS of 350 engines of this model. Let X = the number that operate for an hour without failure. (a) Explain why X is a binomial random variable. (b) Find the mean and standard deviation of X. Interpret each value in context. (c) Two engines failed the test. Are you convinced that this model of engine is less reliable than its supposed to be? Compute P(X 348) and use the result to justify your answer.

ANSWER:

Step 1 of 5

Given,

The probability of aircraft engine to perform properly for an hour of flight,

The no. of engines tested,

Event: X = the number that operate for an hour without failure.

Let’s determine the following using these data:

 

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