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 68.26% of the batteries failed between what two values?

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

about 99.97% of the batteries failed between what two values?

68.2% of the batteries failed between 17.8 and 20.2 hours.

95.44% of the batteries failed between 16.6 and 21.4 hours.

99.97% of the batteries failed between 15.4 and 22.6 hours.

Step-by-step explanation:

The 68-95-99.7 states that, for a normally distributed sample:

68.26% of the measures are within 1 standard deviation of the sample.

95.44% of the measures are within 2 standard deviations of the sample.

99.97% of the measures are within 3 standard deviations of the sample.

In this problem, we have that:

Mean of 19 hours, standard deviation of 1.2 hours.

About 68.26% of the batteries failed between what two values?

This is within 1 standard deviation of the mean. So 68.2% of the batteries failed between 17.8 and 20.2 hours.

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

This is within 2 standard deviations of the mean. So 95.44% of the batteries failed between 16.6 and 21.4 hours.

About 99.97% of the batteries failed between what two values?

This is within 3 standard deviations of the mean. So 99.97% of the batteries failed between 15.4 and 22.6 hours.