Question

According to the manufacturer, an optical fiber has 7 defects
every 3.5 kilometers. Calculate the probability that you will find
minus 1 defect in 350 meters.

From the previous problem, imagine that you did not find any flaws
in the first 250 meters. Calculate how many more meters must be examined in order for the probability of finding the first
defect is 90%.

Answer 1

rate = 7/3.5 = 2 defect/km

a)

lambda = 2 * 0.35 = 0.7

P(X = 1) = e^(- $\lambda$ ) $\lambda$ = 0.7 * e^(-0.7) = 0.3476

b)

for 250 meter

$\lambda$ = 2 * 0.25 = 0.5

P(Y = 0) = e^(-0.5) = 0.6065306

c)

1-e^(-2* l) = 0.9

l = 1.1513

= 1151.3 meter

additional distance = 1151.3 - 250 = 901.3 meter