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.
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
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