Weak spots occur in a certain manufactured tape at random, but at a constant rate of 1 per 100 metres. What is the probability that:
(a) A 240 metre roll of tape will have at most 2 weak spots?
(b) A 120 metre roll of tape will have no weak spots?
(c) In a box of five (5) 120-metre rolls of tape, at least 4 of them will have no weak spots in them at all?
(a)
Let X be the number of Weak spots in k metres of tape.
Average Rate of weak sopts = 1/100 per metres
X ~ Poisson(
= k/100)
For 240 metre roll of tape, X ~ Poisson(
= 2.4)
P(X
2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.09071795 + 0.21772309 + 0.26126771
= 0.5697
(b)
For 120 metre roll of tape, X ~ Poisson(
= 1.2)
P(X = 0)
= 0.3012
(c)
Let Y be the number of boxes with no no weak spots in them.
Y ~ Binomial(n = 5, p = 0.3012)
P(Y
4) = P(Y = 4) + P(Y = 5)
= 0.0312
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