how to find Standard Deviation from a percentile range

Question

Suppose a normal model with a mean of 60 units. What is the standard deviation if 90% of production is at most 100 units?

Answer 1

Z for P=.9000 = 1.28 (from the Z table)

Using the formula Z= (X-μ)/σ we can substitute the known values...

Z= 1.28

μ = 60 units

x= 100 units

1.28 =(100-60)/σ

Since only σ remains as an unknown we can solve for it...

1.28 =(40)/σ then multiply both sides by σ to get...

σ1.28 =(40) then divide both sides by 1.28 to isolate σ

σ = 40/1.28 = 31.25

σ=31.25

I hope that helps!