Question

Flaws along a magnetic tape follow a Poisson distribution with a mean of 0.2 flaw per meter. Let X denote the distance between two successive flaws. (a) What is the mean of X? (b) What is the probability that there are no flaws in 10 consecutive meters of tape? (c) Does your answer to part (b) change is the 10 meters are not consecutive? (d) How many meters of tape need to be inspected so that the probability that at least one flaw is found is 90%? HINT: Compute the 90th percentile for the distribution of X.

Answer 1

a)

mean μ =

1/λ=β =

5.000

b)

probability =

P(X>10)=

1-P(X<10)=

1-(1-exp(-0.2*10))=

0.1353

c)

No

d)

pth percentile =-ln(1-p)/λ =-β*ln(1-p)

therfore 90th percentile =

-5*ln(1-90/100)=

11.5129 meter