Answer:
a) P = 0.29
b) P = 0.32
c) median = 8.3
Explanation:
We have an average distance of 12 m, therefore:
12 = 1/λ
Clearing λ:
λ = 1/12
let "x" be the distance between the flaws, we have:
a)
Let P be the probability that the distance between two flaws is 15 m:
P(x>15) = 1-P(x<15) = 1-(1-e^(λ*x)) = e^(-15/12) = 0.29
b)
Let P be probability that the distance between two flaws is between 8 and 20 m:
P(8<x<20) = P(x<20) - P(x<8) = (1-e^(-20/12)) - (1-e^(-8/12)) = e^(-8/12) - e^(-20/12) = 0.32
c)
The median distance between flaws is equal to:
P(x<median) = 0.5
1-e^(-median/12) = 0.5
e^(-median/12) = 0.5
-median/12 = ln(0.5)
median = ln(0.5) * (-12) = 8.3
