Here is the question:
Chip dies are manufactured in a facility where it was observed that the width of the die is normally distributed with mean 5mm and standard deviation $\sigma$. The manufacturer wants to guarantee that no more than 1 out of 100 dies fall outside the range of (5mm +/- 0.5mm). What should be the maximal standard deviation $\sigma$ of this manufacturing process?
My attempt at a solution:
I figured I could use the central limit theorem and Markov's inequality for this one:
thus-
Pr{die will be in range} = 99/100
I assumed that this should be a normal R.V. (because using a Poisson R.V. to solve this would be tedious)
And now I'm horribly stuck. Any advice as to where I went wrong?
Thank you.