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Statistics: Informed Decisions Using Data | 4th Edition | ISBN: 9780321757272 | Authors: Michael Sullivan, III
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The Empirical Rule The distribution of the length of bolts

Chapter 3, Problem 32E

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QUESTION:

Problem 32E

The Empirical Rule The distribution of the length of bolts has a bell shape with a mean of 4 inches and a standard deviation of 0.007 inch.

(a) About 68% of bolts manufactured will be between what lengths?

(b) What percentage of bolts will be between 3.986 inches and 4.014 inches?

(c) If the company discards any bolts less than 3.986 inches or greater than 4.014 inches, what percentage of bolts manufactured will be discarded?

(d) What percentage of bolts manufactured will be between 4.007 inches and 4.021 inches?

Questions & Answers

QUESTION:

Problem 32E

The Empirical Rule The distribution of the length of bolts has a bell shape with a mean of 4 inches and a standard deviation of 0.007 inch.

(a) About 68% of bolts manufactured will be between what lengths?

(b) What percentage of bolts will be between 3.986 inches and 4.014 inches?

(c) If the company discards any bolts less than 3.986 inches or greater than 4.014 inches, what percentage of bolts manufactured will be discarded?

(d) What percentage of bolts manufactured will be between 4.007 inches and 4.021 inches?

ANSWER:

Answer

Step 1 of 4

(a)

The distribution of the length of bolts has a bell shape with a mean of 4 inches and a standard deviation of 0.007 inches.

About 68% of bolts manufactured will be between what lengths?

The Empirical Rule:

If a distribution is roughly bell-shaped, then

Approximately 68% of the data will lie within 1 standard deviation of the mean. That is, approximately 68% of the data lies between  and .

68% of bolts manufactured are within 1 standard deviation of the mean.

Hence we can write the lengths of bolts between  and

 and

 and

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