# The weights of certain machine components are normally distributed with a mean of 8.5 g and a standard deviation of 0.09 g. Find the two weights that separate the top 3% and the bottom 3%. These weights could serve as limits used to identify which components should be rejected. Round to the nearest hundredth of a gram. Find the indicated probability, showing an appropriate calculator sequence.

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The weights of certain machine components are normally distributed with a mean of 8.5 g and a standard deviation of 0.09 g. Find the two weights that separate the top 3% and the bottom 3%. These weights could serve as limits used to identify which components should be rejected. Round to the nearest hundredth of a gram.

Find the indicated probability, showing an appropriate calculator sequence.

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Step 1

It is given that the mean and standard deviation are 8.5 and 0.09, respectively.

Step 2

The area of 0.03 to the left of z is –1.88 using standard normal table.

The weight that separate the bottom 3% is obtained as follows:

Step 3

area of 0.03 to the right of z is 1.88 using standard normal table.

The weight that separate the top 3% is obtained as follows:

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