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hollandhogenson
01.04.2021 •
Mathematics
The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.11 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 9% and the bottom 9%. 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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Ответ:
The diameter that separates the bottom 9% is 5.02 millimeters.
The diameter that separates the top 9% is 5.2 millimeters.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 5.11 millimeters and a standard deviation of 0.07 millimeters.
This means that![\mu = 5.11, \sigma = 0.07](/tpl/images/1235/7612/177a4.png)
Bottom 9%:
The 9th percentile, which is X when Z has a pvalue of 0.09. So X when Z = -1.34.
The diameter that separates the bottom 9% is 5.02 millimeters.
Top 9%:
The 100 - 9 = 91th percentile, which is X when Z has a pvalue of 0.91. So X when Z = 1.34.
The diameter that separates the top 9% is 5.2 millimeters.
Ответ:
m=4
Step-by-step explanation:
Using the slope formula: y2 - y1 / x2 - x1
m = 4 - (-4) / 5 - 3
m = 8 / 2
m = 4