Manufacturer Alpha produces a continuous band of videotape that is used to fill

Question

Manufacturer Alpha produces a continuous band of videotape that is used to fill your unit's supply of videocassettes. Assume the number of flaws in the videotape follows a Poisson distribution and that there are on average 4 flaws per 100 linear feet. a) What is the probability that in a 50 foot length of videotape there will be no flaws? b) What is the probability that in a 50 foot length of videotape there will be at least 3 flaws? c) What is the probability that in a 50 foot length of videotape there will be at least 30 flaws?

Explanation / Answer

Assume the number of flaws in the videotape follows a Poisson distribution
and that there are on average 4 flaws per 100 linear feet

a.
mean rate for 50 foot length of videotape = 2
length of videotape there will be no flaws =
P( X = 0 ) = e ^-2 * 2^0 / 0! = 0.1353

b.
there will be at least 3 flaws = P( X < 3) = P(X=2) + P(X=1) + P(X=0)
= e^-2 * 2 ^ 2 / 2! + e^-2 * ^ 1 / 1! + e^-2 * ^ 0 / 0!
= 0.6767
P( X > = 3 ) = 1 - P (X < 3) = 0.3233

c.
P( X > = 30 ) = 1 - P (X < 30) = 0

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.