# Homework Help: Gumbel dustribution

1. Mar 17, 2007

### mikeliebelt

1. The problem statement, all variables and given/known data
I am not very familiar with this distribution.It asking me the proportion of switches that fails to meet specification.The questoin is:

The specification for the output rise time of a bipolar Hall switch is between 0.23 and 0.27 microseconds. Fly Electronics can only achieve a process capability ( ) of 0.8.
(i) If Fly electronics achieve a process mean of 0.25, what proportion of switches would fail to meet specification if rise times are normally distributed?
(ii) Suppose Fly Electronics manufactured switches with a mean that is off centre and only achieve a process performance ( ) of 0.7. What proportion of switches would fail to meet specification if rise times are normally distributed?

(iii) If Fly electronics achieve a process mean of 0.25, what proportion of switches would fail to meet specification if rise times have a Gumbel distribution?

I found out that standard deviation is 8.33*10^-3.I did first 2 parts,not sure how to do 3.

2. Relevant equations

Gumbel distr. has cdf
F(x)=exp(-exp(-(x-e)/d))
mean=e+0.57722*d
sd=1.28255*d

3. The attempt at a solution