Question

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 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.

Answer 1

Given,

= 5.18 , = 0.07

We have to calculate two values that separates top 3% and bottom 3%, that is we have to calculate middle of

94% data.

We use formula as

z *

Where - z * is bottom value and + z * is top value.

From Z table,

z critical value at 0.03 significance level = 1.8808

Lower value that separates bottom 3% = - z * = 5.18 - 1.8808 * 0.07 = 5.05

Upper value that separates top 3% = + z * = 5.18 + 1.8808 * 0.07 = 5.31

Two diameters that separates to 3% and bottom 3% are 5.31 and 5.05 respectively.