The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.725.72 millimeters and a standard deviation of 0.070.07 millimeters. Find the two diameters that separate the top 5%5% and the bottom 5%5%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.

Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Top 5%:

X when Z has a pvalue of 0.95. So X when Z = 1.645

Bottom 5%:

X when Z has a pvalue of 0.05. So X when Z = -1.645

Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.

the function makes a strait line horizontally with no x intercept but a y intercept at 9.