A company that manufactures rivets believes the shear strength (in pounds) is modeled by [tex]N(800, 47)[/tex]. Draw the normal model for these rivets. Clearly label it, showing what the 68-95-99.7 rule predicts.

Question

10-02-2024
Engineering

College

We appreciate your visit to A company that manufactures rivets believes the shear strength in pounds is modeled by tex N 800 47 tex Draw the normal model for these. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A company that manufactures rivets believes the shear strength (in pounds) is modeled by [tex]N(800, 47)[/tex]. Draw the normal model for these rivets. Clearly label it, showing what the 68-95-99.7 rule predicts.

Answer :

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Final answer:

The shear strength of rivets can be modeled by a normal distribution. The normal model predicts that a certain percentage of rivets will have shear strengths within a certain range. The 68-95-99.7 rule provides estimates for these ranges.

Explanation:

Normal Model for Shear Strength of Rivets

The shear strength of rivets can be modeled by a normal distribution with a mean of 800 pounds and a standard deviation of 47 pounds. The normal model is a bell-shaped curve that represents the probability distribution of the shear strength of the rivets.

The 68-95-99.7 rule, also known as the empirical rule, predicts that approximately:

68% of the rivets will have shear strengths within one standard deviation of the mean, which is between 753 pounds and 847 pounds.
95% of the rivets will have shear strengths within two standard deviations of the mean, which is between 706 pounds and 894 pounds.
99.7% of the rivets will have shear strengths within three standard deviations of the mean, which is between 659 pounds and 941 pounds.

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