Question

Piston rings are mass-produced. The target internal diameter is 45mm but records show
that the diameters are normally distributed with mean 45mm and standard deviation 0.05
mm. An acceptable diameter is one within the range 44.95 mm to 45.05 mm.
(i) What proportion of the output is unacceptable?
(ii) Above what diameter do the 40% largest diameters lie?

Answer 1

X : internal diameter of Piston rings.

X ~ N(45,0.05)

a).the proportion of acceptable output is:-

[ using standard normal table]

the proportion of  the output is unacceptable is:-

b).let a be the diameter above which the 40% largest diameters lie.

according to the problem:-

[ in any blank cell of excel type =NORMSINV(0.60) press enter]

the 40% largest diameters lie above 45.0127 mm

***in case of doubt, comment below. And if u liked the solution, please like.