Question

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.72 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 5% and the bottom 5%

. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.

Answer 1

Solution :

Given that,  

mean = = 5.72

standard deviation = = 0.07

i

Using standard normal table ,

P(Z > z) = 5%

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.05

P(Z < 1.65) = 0.95

z = 1.65

Using z-score formula,

x = z * +

x = 1.65 * 0.07 + 5.72 = 5.84

ii

Using standard normal table ,

P(Z < z) = 5%

P(Z < -1.65) = 0.05

z = -1.65

Using z-score formula,

x = z * +

x = -1.65 * 0.07 + 5.72 = 5.60

The two diameters that separate 5.84 , 5.60