When commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable,or critical. The history of...
When commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable,or critical. The history of a particular fleet indicates that 70% of the planes inspected have no wing cracks, 25% have detectable wing cracks, and 5% have critical wing cracks. Seven planes are randomly selected.
(a) Find the probability that one has a critical crack, two have
detectable cracks, and four have no cracks.
(b) Find the probability that the number of planes with no wing
cracks is at least twice as many of the number of planes with
detectable or critical wing cracks.
Homework Answers
a)
from Multinomial distribution:
probability that one has a critical crack, two have detectable cracks, and four have no cracks
=(7!/(1!*2!*4!))*(0.05)*(0.25)2*(0.70)4 = 0.0788
b)let X be number with no wing cracks,
probability that the number of planes with no wing cracks is at least twice as many of the number of planes with detectable or critical wing cracks =P(X>=5) =P(X=5)+P(X=6)+P(X=7)
=(7C5)*(0.70)5(0.3)2+(7C5)*(0.70)6(0.3)1+(7C5)*(0.70)7(0.3)0=0.6471
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