Poisson distribution

For the third part

I know that 1 - Pr(0 Failures) = 0.5

How do I find N and u

Thanks

For the third part

I know that 1 - Pr(0 Failures) = 0.5

How do I find N and u

Thanks

Go to the definition of the Poisson, what's P(X=0) in terms of the parameter for the Poisson? Slap it into your equation and ...

Then since 30,000 has a parameter of 0.3, what value (N) would give this parameter (the one you just worked out).

Let X = number of catastrophic failures in a production with N assemblies

So, u is just the mean, or expected value: all you have to do is multiply N by 1/100000.
>> u = (1x10-5)N
Therefore:
X ~ Po[(1x10-5)N]

Now, to find N, we are told that P(X >= 1) = 0.5.
But, P(X >= 1) = 1 - P(X = 0)
Now this is were your Core maths skills come in handy as it begins to get a bit messy:
image

Forgot to round to 4 sig figs, sorry

May I ask where you got that worksheet from?

Here is another similar question I get 3.5 days for the last part is this correct.

Agreed.