Solved: The Empirical Rule The distribution of the length

Problem 32AYU

 Problem

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?

                                                            Step by step solution

Step 1 of 4

(a)

Given,

Mean, = 4 inch

Standard deviation,  = 0.007 inch

To find the lengths of 68% bolts we will have to determine 1st standard deviation within 68%, as shown in the above Figure, ie; approximately 68% of the data lie between  -  and  + .

 -  = 4 - 0.007 = 3.993

 +  = 4 + 0.007 = 4.007