A paint manufacturer discovers that the mean volume of paint in a gallon-sized pail is 1 gallon with a standard deviation of 0.05 gallons. The paint volumes are approximately bell-shaped. Estimate the percent of pails with volumes between 0.90 gallons and 1.10 gallons.
A)95%
B)5%
C)almost all (greater than 95%)
D)68%

Question

Quizplus · Accepted Answer

This scenario is described by the empirical rule (or 68-95-99.7 rule) for bell-shaped distributions, which states that approximately 95% of the data falls within two standard deviations of the mean. Since 0.90 gallons and 1.10 gallons are each 0.10 gallons away from the mean (1 gallon), and the standard deviation is 0.05 gallons, this range covers two standard deviations on either side of the mean (2 x 0.05 = 0.10). Therefore, approximately 95% of the pails will have volumes between 0.90 gallons and 1.10 gallons.

A Paint Manufacturer Discovers That the Mean Volume of Paint