Question

The diameters of bolts produced in a machine shop are normally distributed with a mean of 6.4 millimeters and a standard deviation of 0.06 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

6.30 millimeters and 6.50 millimeters.

Answer 2

The bolts with diameter less than 5.57 millimeters and with diameter greater than 5.85 millimeters should be rejected.

Explanation:

We have been given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviation of 0.08 millimeters.

Let us find the sample score that corresponds to z-score of bottom 4%.

From normal distribution table we got z-score corresponding to bottom 4% is -1.75 and z-score corresponding to top 4% or data above 96% is 1.75.

Upon substituting these values in z-score formula we will get our sample scores (x) as:

Therefore, the bolts with diameters less than 5.57 millimeters should be rejected.

Now let us find sample score corresponding to z-score of 1.75 as upper limit.

Therefore, the bolts with diameters greater than 5.85 millimeters should be rejected