Find standard deviation when there is no specific data

#1
It is said,

In order to profitably manufacture a product, you determine that you must have a scrap rate no greater than 5%. In other words, at least 95% of your product must be accepted. If the specified range for the product is 12.0 inches +/- 0.1 inch, what standard deviation must you manufacture at in order to be profitable?



So, I don't know how to get it.
I think it is 0.05 because:
the range is 11.9 and 12.1 , and 12.0 +/- (0.05*2) is equal to range?
(empirical rule?)

Thanks
 

Karabiner

TS Contributor
#3
Assuming a normal distribution, the 95% interval is 12 +/- 1.96 SD = 12 +/- 0.1 .
It's 0.05 if rounded, but maybe they want a more exact figure.

Kind regards

K.
 
#6
I'm confused. Where does 1.96 come from? I'm assuming 0.05 is the percent of scrap? I don't understnd, please help

Assuming a normal distribution, the 95% interval is 12 +/- 1.96 SD = 12 +/- 0.1 .
It's 0.05 if rounded, but maybe they want a more exact figure.