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A process manufactures ball bearings with diameters that are normally distributed with mean 25.14 mm and standard deviation 0.08 mm. NOTE: T
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A process manufactures ball bearings with diameters that are normally distributed with mean 25.14 mm and standard deviation 0.08 mm. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on
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2021-07-24T02:33:59+00:00
2021-07-24T02:33:59+00:00 1 Answers
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Answer:
The diameter is in the 77th percentile.
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 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.
25.14 mm and standard deviation 0.08 mm.
This means that![Rendered by QuickLaTeX.com \mu = 25.14, \sigma = 0.08](https://documen.tv/wp-content/ql-cache/quicklatex.com-91b7c0c1adaf4a0babebacb1d019abac_l3.png)
A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on?
This is the pvalue of Z when X = 25.2. So
The diameter is in the 77th percentile.