Question

A manufacturer produces gears for use in an engine's transmission that have a mean diameter of 10.00 mm and a standard deviation of 0.05 mm. The lengths of these diameters have a normal distribution. What is the diameter that separates the largest 20% of diameters from the rest? 9.958 0.4772 9.974 10.026 10.042 None of these

Answer 1

Solution:-

mean = $\mu$ = 10.00

standard deviation = $\sigma$ = 0.05

P(Z > z ) = 0.20

1- P(z < z) =0.20

P(z < z) = 1-0.20 = 0.80

z = 0.84

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 0.84*0.05 +10

x = 10.042

Answer = 10.042