For a particular D-cell alkaline battery, the mean life is 19 hours. The useful life of the battery follows a normal distribution with a standard deviation of 1.2 hours.

Question

As part of its quality assurance program, the Exide Battery Company conducts

tests on battery life. For a particular D-cell alkaline battery, the mean life is 19 hours.

The useful life of the battery follows a normal distribution with a standard deviation of 1.2

hours. Answer the following questions.

1. About 68 percent of the batteries failed between what two values?

2. About 95 percent of the batteries failed between what two values?

3. About 99.7 percent of the batteries failed between what two values?

Answer 1

68% of the batteries failed are within 1 standard deviation of the mean, so they are within 19 +/- 1.2

95% of the batteries failed are within 1 standard deviation of the mean, so they are within 19 +/- 2.4

99.7% of the batteries failed are within 1 standard deviation of the mean, so they are within 19 +/- 3.6