Question

The diameters of bolts produced in a machine shop are normally distributed with a mean of 6.26 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 3% and the bottom 3%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.

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________ milimeters and _______millimiters

Normal Table 0 to z

Normal Table -∞ to -z

Normal Table -∞ to z

Answer 1

Given = 6.26 and = 0.07

When using the normal distribution we use z scores

The Lower p value = 0.03 and the Upper p value = 1 - 0.03 = 0.97

The Z score at p = 0.03 and 0.97 are -1.8808 and +1.8808 respectively.

The Lower value: (X - 6.26)/0.07 = -1.8808. Solving for X, X = (-1.8808* 0.07) + 8.4 = 6.12 mm

The Upper value: (X - 6.26)/0.07 = 1.8808. Solving for X, X = (1.8808* 0.07) + 8.4 = 6.39 mm

The limits are between 6.12 mm and 6.39 mm