Question

Say you have 30 resistors with a nominal value of 100 Ohms. What does the standard deviation need to be for 99% of the resistors to be within ±10% of the nominal value?

Answer 1

middle proportion=   0.99                  
proportion left    0.01   is equally distributed both left and right side of normal curve               
z value at   0.005   = ±   2.58   (excel formula =NORMSINV(   0.01   / 2 ) )

z = ( x - µ ) / (σ/√n)
σ=(x-µ)*√n / z

σ=(-10)*√30 / -2.58  

we get,

σ=21.2639

so, std dev = 21.2639