The lengths of screws produced by a machine are normally distributed with a mean of 3 inches and a standard deviation of .2 inches. Therefore, we know:
A) that approximately 68 percent of all screws have lengths between 2.8 and 3.2 inches
B) that approximately 95 percent of all screws have lengths between 2.8 and 3.2 inches
C) that just about all screws have lengths between 2.8 and 3.2 inches
D) that approximately 98 percent of all screws have lengths between 2.8 and 3.2 inches
E) none of these

Question

Quizplus · Accepted Answer

This follows the empirical rule (68-95-99.7 rule) for normal distributions, which states that approximately 68% of the data falls within one standard deviation (±0.2 inches in this case) from the mean (3 inches), thus between 2.8 and 3.2 inches.

The Lengths of Screws Produced by a Machine Are Normally