Question

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 0.95 gallons and 1.05 gallons.

Answer 1

Answer:

Approximately 68%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 1, standard deviation = 0.05.

Estimate the percent of pails with volumes between 0.95 gallons and 1.05 gallons.

0.95 = 1 - 0.05

1.05 = 1 + 0.05

So within 1 standard deviation of the mean, which by the Empirical Rule, is approximately 68% of values.