An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44% of the batteries failed between what two values?

a. 8.9 and 18.9

b. 12.2 and 14.2

c. 14.1 and 22.1

d. 16.6 and 21.4

d. 16.6 and 21.4

Step-by-step explanation:

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

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

95.44% of the measures are within 2 standard deviation of the mean.

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

In this problem, we have that:

Mean = 19

Standard deviation = 1.2

About 95.44% of the batteries failed between what two values?

Within 2 standard deviations of the mean

19 - 2*1.2 = 16.6

19 + 2*1.2 = 21.4

So the correct answer is:

d. 16.6 and 21.4