Defects occur along the length of cable at an average of 5 defects per 4,000 feet. ASsume that the probability of k defects in t feet of cable is given by the probability mass function: e -(5t/ 4000) (5 t/ 4,000 ) k P(k defects ) = . k! for k = 0, 1, 2, .. Find the probability that a 3,200 foot cable will have а. at most three defects b. at least four defects С. between 1 to 5 (inclusive) defects

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Defects occur along the length of cable at an average of 5 defects per 4,000 feet. Assume that the probability of k defects in t feet of
cable is given by the probability mass function:
-( 5t/ 4000)
'(5t/4,000)k
e
P(k defects ) =
k!
for k = 0, 1, 2, .. Find the probability that a 3,200 foot cable will have
a.
at most three defects
b.
at least four defects
C.
between 1 to 5 (inclusive) defects
Transcribed Image Text:Defects occur along the length of cable at an average of 5 defects per 4,000 feet. Assume that the probability of k defects in t feet of cable is given by the probability mass function: -( 5t/ 4000) '(5t/4,000)k e P(k defects ) = k! for k = 0, 1, 2, .. Find the probability that a 3,200 foot cable will have a. at most three defects b. at least four defects C. between 1 to 5 (inclusive) defects
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