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Statistics / Essentials of Probability & Statistics for Engineers & Scientists 1 / Chapter 5 / Problem 5.20

Essentials of Probability & Statistics for Engineers & Scientists | 1st Edition | ISBN: 9780321783738 | Authors: Ronald E. Walpole, Raymond Myers, Sharon L. Myers, Keying E. Ye

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A type of thread is being studied for its tensile strength

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QUESTION:

A type of thread is being studied for its tensile strength properties. Fifty pieces were tested under similar conditions, and the results showed an average tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. Assuming a normal distribution of tensile strengths, give a lower 95% prediction limit on a single observed tensile strength value. In addition, give a lower 95% tolerance limit that is exceeded by 99% of the tensile strength values.

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QUESTION:

A type of thread is being studied for its tensile strength properties. Fifty pieces were tested under similar conditions, and the results showed an average tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. Assuming a normal distribution of tensile strengths, give a lower 95% prediction limit on a single observed tensile strength value. In addition, give a lower 95% tolerance limit that is exceeded by 99% of the tensile strength values.

ANSWER:

Step 1 of 6

We have,

From , we have:

Implies,

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