I am having problems with parts b and c in this problem and would appreciate any helpful feedback. Thank you!
A certain type of insect screen 6 feet wide has, on average, 4 flaws in a 150 foot roll.
a.) What is the probability that the first 50 feet in a roll contains only 1 flaw?
I found that there were 2/75 flaws per feet which means there are 4/3 flaws per 50 feet and the probability that the first 50 feet contains 1 flaw is 0.351 (I found this using the p.m.f. for the Poisson distribution where lambda=4/3 and x=1).
b.) What is the distribution of W, the number of feet we would have to check (from the beginning of the roll) before we see the second flaw?
This is supposedly a gamma distribution, but can someone explain to me why it is? And what the parameters would then be for this gamma distribution?
c.) Find P(W>100)
I am not sure how to set up this part.
A certain type of insect screen 6 feet wide has, on average, 4 flaws in a 150 foot roll.
a.) What is the probability that the first 50 feet in a roll contains only 1 flaw?
I found that there were 2/75 flaws per feet which means there are 4/3 flaws per 50 feet and the probability that the first 50 feet contains 1 flaw is 0.351 (I found this using the p.m.f. for the Poisson distribution where lambda=4/3 and x=1).
b.) What is the distribution of W, the number of feet we would have to check (from the beginning of the roll) before we see the second flaw?
This is supposedly a gamma distribution, but can someone explain to me why it is? And what the parameters would then be for this gamma distribution?
c.) Find P(W>100)
I am not sure how to set up this part.