Question

Murphy’s Law: The Air Force has ordered a new fighter jet from Lockheed Martin with contains 1000 critical engineering components. Tests have shown that each of these parts will fail independently with a probability of p = 0.001. In the design team they have to decide how much redundancy to build into the system. (a) Define a random variable X which counts the number of components which fail on the jet. What distribution does X have, and what are the parameters of the distribution? (b) If they add no redundancy into the system, so that the jet will fail if ANY of these 100 critical components fails what is the probability that the jet fails? (c) Given these numbers they decide to add some redundancy so that the jet will continue to work as long as less than k components fail. What is the minimum k where the probability for the jet to fail is less than P(X > k) < 0.001

Answer 1

a)

total no. of components = 1000

probability of failure of any component=0.001

X= the numbr of components that fails. Then X is a binomial variable with parameters,

and

b)

the jet will fail if ANY of these 100 critical components fails. so the probability that the jet fails is equivalent to,

c)

we have to find minimum k such that,

[Z is standard normal]

from the normal table we found that,