# Thread: Need help understanding these problems

1. ## Need help understanding these problems

1. A factory has a delicate process that is affected by weather. If it rains, decrease the humidity inside the factory to continue operations. Since inside the factory the rain is no heard it is known that the probability of the work being damaged given that nobody noticed in time is 33%. If you have 85 rainfalls in a year calculate the expected number of damaged works and variance.

2. On average, every six minutes a car passes by a sector in which it plans to build a tunnel. The passage of many vehicles indicate risk of congestion in the new construction. The engineers in charge of the project need to determine whether the probability that in one hour more than 5 vehicles that circulate by the sector is less than 0.04.

2. ## Re: Need help understanding these problems

problem two is a poisson distribution. The only trick here is to convert the rate of 1/6 car per minute to the # of cars per hour. Once you have the proper distribution just evaluate it's CDF at 5.

in problem 1 we assume that the whole days work is lost 33% of the time when it rains? So we are basically trying to determine the number of days out of 85 that the humidity messes up and everything is ruined.

This is a binomial distribution. with N=85, and p=33%=0.33 you can look up the distribution and derive the mean and variance easily enough. You're going to get numbers that are in units of #days of failure.

3. ## Re: Need help understanding these problems

Thx I worked on the first one, but the second one Im still having trouble with he secong one can't get the exact value

4. ## Re: Need help understanding these problems

Originally Posted by luis0426
Thx I worked on the first one, but the second one Im still having trouble with he secong one can't get the exact value
were you able to calculate $\lambda$ for x in hours? Do you have some way of evaluating the CDF of the poisson distribution?

5. ## Re: Need help understanding these problems

I knid of know how to solve it, I think my problem lies in how to work with this The only trick here is to convert the rate of 1/6 car per minute to the # of cars per hour. dont know if im doing it rigth

6. ## Re: Need help understanding these problems

Originally Posted by luis0426
I knid of know how to solve it, I think my problem lies in how to work with this The only trick here is to convert the rate of 1/6 car per minute to the # of cars per hour. dont know if im doing it rigth
so what did you come up with for $\lambda$ in units of cars per hour?

7. ## Re: Need help understanding these problems

1car/6min (60min/1h) = 6 cars per hour, dont know how to work with that and the determine whether the probability that in one hour more than 5 vehicles that circulate by the sector

8. ## Re: Need help understanding these problems

cough... how many 6 minute periods in 1 hr?

I don't know what circulate the sector means.. I just assume it means pass by, i.e. is an occurrence.

9. ## Re: Need help understanding these problems

Im a bit confused too, how would you solve to get λ

10. ## Re: Need help understanding these problems

1 car every 6 minutes ---> 10 cars an hour ----> $\lambda=10$

11. ## Re: Need help understanding these problems

That much I got my problem lies in the probability that in one hour more than 5 vehicles that circulate by the sector is less than 0.04, how does the 5 factor in here, I know that P(x=0.4,λ), how does the 5 factor in the problem.

12. ## Re: Need help understanding these problems

Originally Posted by luis0426
That much I got my problem lies in the probability that in one hour more than 5 vehicles that circulate by the sector is less than 0.04, how does the 5 factor in here, I know that P(x=0.4,λ), how does the 5 factor in the problem.
Pr[6 more cars go by] = 1 - Pr[5 or less cars go by] = F(5) where F(x) is the CDF of the Poisson distribution with parameter $\lambda=10$

13. ## Re: Need help understanding these problems

I got it like this P(x>6) = 1-P(x=0)-P(x=1-P(x=2)-P(x=3)-P(x=4)-P(x=5), but know if parameter λ=10 and x is 0 through 5, how do I work with the 0.4 here

14. ## Re: Need help understanding these problems

Originally Posted by luis0426
I got it like this P(x>6) = 1-P(x=0)-P(x=1-P(x=2)-P(x=3)-P(x=4)-P(x=5), but know if parameter λ=10 and x is 0 through 5, how do I work with the 0.4 here
you don't work it in there. The engineer just wants to check that the actual probability of that many cars is < 0.04.

He's in for a disappointment.