the diameters of ball bearings are distributed normally. the mean diameter is 71 millimeters and the standard deviation is 4 millimeters. find the probability that the diameter of a selected bearing is greater than 66 millimeters. round your answer to four decimal places.

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27-10-2022
Mathematics

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the diameters of ball bearings are distributed normally. the mean diameter is 71 millimeters and the standard deviation is 4 millimeters. find the probability that the diameter of a selected bearing is greater than 66 millimeters. round your answer to four decimal places.

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qwmaroon qwmaroon · Answer 1 · 2022-10-31T13:09:26-04:00

The probability that the diameter of a selected bearing is greater than 123 millimeters is 0.8944 = 89.4400%.

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

In a set the Z-score of a measure X is given by:

Z = ( X - μ )/σ

Here , μ is Mean, σ is the standard deviation and X is Z-score of a measure.

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

We have, μ = 71 millimeters and σ = 4millimeters

The probability that the diameter of a selected bearing is greater than 66 millimeters,

This is 1 subtracted by the p-value of Z when X = 66. So

Z = ( 66 - 71 )/4

Z = -5/4

Z = -5/4 has a p-value of 0.1056.

1-0.1056 = 0.8944

0.8944 = 89.4400% is the probability that the diameter of a selected bearing is greater than 66 millimeters.

To know about Z-score refer to the link:

https://brainly.com/question/25638875

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