I have the following question:

A machine makes slots of a duralumin forging. The width of the slot is normally distributed with mean of 0.900cm and standard deviation of 0.003cm. The specification limits were given as 0.900 ± 0.007, i.e. forgings outside this interval are

considered defective.

(i) What percentage of the forgings will be defective?

(ii) On average how many forgings will be made until a defective forging is found?

(iii) How much should we fine-tune the machine (i.e. reduce the standard deviation) in order to reduce the probability of a defective forging to 1%.

So for (i) is did:

X~(0.9,0.000009)

P( 0.893<= x <= 0.907)

which gave me a value of 0.9576, so (i) is 1-0.9576 = 0.0424

(ii) Is this the expected value for the geometric distribution?

And Im stuck at the final part.