S2 Poisson/ Binomial
From Jan 2010:
3. A robot is programmed to build cars on a production line. The robot breaks down at random at a rate of once every 20 hours. (a) Find the probability that it will work continuously for 5 hours without a breakdown. (3)
Could someone explain why it's incorrect to use (19/20)^5 here? I understand how to use poisson, I'm just not clear on why binomial wouldn't work here.
3. A robot is programmed to build cars on a production line. The robot breaks down at random at a rate of once every 20 hours. (a) Find the probability that it will work continuously for 5 hours without a breakdown. (3)
Could someone explain why it's incorrect to use (19/20)^5 here? I understand how to use poisson, I'm just not clear on why binomial wouldn't work here.
Original post by P1NNumber
From Jan 2010:
3. A robot is programmed to build cars on a production line. The robot breaks down at random at a rate of once every 20 hours. (a) Find the probability that it will work continuously for 5 hours without a breakdown. (3)
Could someone explain why it's incorrect to use (19/20)^5 here? I understand how to use poisson, I'm just not clear on why binomial wouldn't work here.
3. A robot is programmed to build cars on a production line. The robot breaks down at random at a rate of once every 20 hours. (a) Find the probability that it will work continuously for 5 hours without a breakdown. (3)
Could someone explain why it's incorrect to use (19/20)^5 here? I understand how to use poisson, I'm just not clear on why binomial wouldn't work here.
Your assumption that P(no breakdowns in one hour) = 19/20 is invalid.
If the rate of breakdowns per 20 hours is 1, we are entitled to assume that the rate of breakdowns per hour is 1/20. The distribution we are now dealing with is Po(1/20), in which case P(X = 0) is exp(-1/20), not 19/20. You can then plug that probability into your binomial calculation to give P(no breakdowns in 5 hours) = (exp(-1/20))^5 = exp(-1/4). But this is a bit of a long way round compared to deducing the rate of breakdowns per five hours and using that directly.
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