Question

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?

Answer 1

(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