Question 1121297: 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) if the probability of landing safely must be at least 99.5% what is the minimum value for p ?
b)...
c)...
The question is quoted from the book "Complete Business Statistics" 7th Edition by Sounderpandian (Asian edition)
Chapter 3, problem 3-41 (page no.134)
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it looks like 89% reliability is the magic number.
that will give you an overall probability of 2 or more engines working at the same time of .995115.
anything less than that will result in an overall probability of less than .995.
i used the binomial theorem and kept dropping the individual reliability percent down by 1 until the overall probability became less than 99.5%.
in other words, i started at p = .92, then .91, then .90, then .89, then .88.
.89 was above 99.5% overall.
.88 was below 99.5% overall.
the calculations are shown in the following spreadsheet printouts.
i'm not exactly sure if this is the right formula to use, but if it is, there's a high probability that the answer will be correct.
the binomial formula tells you the probability of x occurrences out of n, given the probability that the event will occur or not occur.
the formula is p(x) = p^x * q^(n-x) * c(n,x).
n is 4 in this problem.
x ranges from 0 to 4.
p is .92 or .91 or .90 or .89 or .88
q is 1 - p
c(n,x) is the numbe of ways you can get sets of x elements out of a set of n elements when order is not important.
that formula is c(n,x) = n! / (x! * (n-x)!)
Answer by ikleyn(52794)  (Show Source):
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