Question

A machine that produces ball bearings has initially been set so that the mean diameter of the bearings it produces is 0.500 inches. A bearing is acceptable if its diameter is within 0.004 inches of this target value. Suppose, however, that the setting has changed during the course of production, so that the distribution of the diameters produced is now approximately normal with mean 0.498 inch and standard deviation 0.002 inch. What percentage of the bearings produced will not be acceptable? (You may need to use a table) . (Round your answer to two decimal places.)

          A machine that produces ball bearings has initially been set so
that the mean diameter of the bearings it produces is 0.500
inches. A bearing is acceptable if its diameter is
within 0.004 inches of this target value. Suppose,
however, that the setting has changed during the course of
production, so that the distribution of the diameters produced is
now approximately normal with mean 0.498 inch and
standard deviation 0.002 inch. What percentage of the
bearings produced will not be acceptable? (You may need to
use a table)
. (Round your answer to two decimal places.)

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Added by Paula H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

11/21/2021

Step 1

The acceptable range is from 0.500 - 0.004 = 0.496 inches to 0.500 + 0.004 = 0.504 inches. Show more…

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A machine that produces ball bearings has initially been set so that the mean diameter of the bearings it produces is 0.500 inches. A bearing is acceptable if its diameter is within 0.004 inches of this target value. Suppose, however, that the setting has changed during the course of production, so that the distribution of the diameters produced is now approximately normal with mean 0.498 inch and standard deviation 0.002 inch. What percentage of the bearings produced will not be acceptable? (You may need to use a table) . (Round your answer to two decimal places.)

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Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:07 In this question here we're given the mean diameter of the bering is it produces is 0 .5 inches.

00:16 And then we have a buren is acceptable if the diameter is within the 0 .004 inches of this target value.

00:25 So the acceptable interval.

00:37 The x here must be between the 0 .5 plus 0 .004 and 0 .5 minus 0 .0 .0 .0 .0.

00:47 X must be between the interval 0 .504.

00:56 And the one on the left will be 0 .5 minus 0 .004.

01:02 It will equal to 0 .46.

01:05 That will be the acceptable interval.

01:07 Now we have the x, it will have followed by the normal with the mean equal to the 0 .498 and the standard division equal to 0 .002.

01:21 Once you find the probability that the brinko will be not acceptable.

01:30 So it just equal to 1 minus the probability is acceptable.

01:35 And then we get equal to 1 minus acceptable if your x must be between the 0 % acceptable.

01:42 0 .496 and the 0 .04.

01:47 Now we need to turn the x here into the standard normal.

01:51 Remind to you that if we have the x minus mean over standard deviation, it will follow by the standard normal.

01:58 Therefore we will have here 1 minus probability.

02:01 The middle one will turn into the z...

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