Question

Flaws in a carpet ten to occur randomly and independently at a rate of two every 100 square feet. What is the probability that:
a) a carpet that is 8 feet by 12 feet contains three flaws

Answer 1

Well, what do you think?

Answer 2

Start by finding the area of the carpet

Answer 3

A=l*w

length=8
width=12

A=8*12
A=?

Answer 4

A=lxw
=8x15
=120

Answer 5

@horsegirl27

Answer 6

Oops, you had 8*15, you want 8*12

Answer 7

Oh you know what in the question i typed 12 its supposed to be 15 sorry for the confusion. But now that I have the area then what? @horsegirl27

Answer 8

So, if a carpet will have 2 flaws every 100 sq ft, and the area is 96 sq ft, is there a chance there will be 3 flaws?

Answer 9

No I guess not because there is not enough area but if the area is 120 which is the 8*15 then it would have enough room to have 3 flaws right? @horsegirl27

Answer 10

I'm not sure. But since your area is 96 sq ft, your answer will be no.

Answer 11

Well, not exactly no. Next you will have to find the probability

Answer 12

If you look at my messages above it says that I made a mistake and that the 12 should be a 15 @horsegirl27

Answer 13

oh right, I'm sorry I thought you meant when you typed it in the problem.

Answer 14

its supposed to be 8*15 so how do I solve this? @horsegirl27

Answer 15

@Shaekitchen
hint:
review Poisson distribution in your notes. \(\lambda\) equals to 2*96/100.

Answer 16

Is that my full answer thought? Im not sure where else to take it? My prof is crap at writing notes I cant understand it.@mathmate

Answer 17

What I am saying is the probability is obtained by the Poisson distribution, with lambda = 0.96*2/100= expected number of flaws for 96 sq.ft, and n=3 (3 flaws).

Answer 18

You have to do a calculation to find P(n)=\(\large \frac{\lambda ^k}{k!}e^{-\lambda}\)
\(\lambda = 2*96/100 =expected number of flaws, k=3 (flaws) )
For further information, read:
http://en.wikipedia.org/wiki/Poisson_distribution

Answer 19

* P(k) = ....