Question

7.) As part of its quality assurance program, the Autolite Battery Company conducted test 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.

a) About 68% of the batteries failed between what two values?

b) About 95% of the batteries failed between what two values?

c) Virtually all of the batteries failed between what two values?

Please show work using Excel.

Answer 1

We have given the normal distribution

Empirical rule

We plug the value of mean and standard deviation

Approximately 68 % batteries will fail between 19 - 1.2 = 17.8 and 19 + 1.2 = 20.2

Answer for a ) part

Approximately 68 % batteries will fail between 17.8 and 20.2 hours

We plug the value of mean and standard deviation

Approximately 95 % batteries will fail between 19 - 2*1.2 = 19 - 2,4 =16.6 and 19 + 2*1.2 = 19 + 2.4= 21.4

Answer for b part

Approximately 95 % batteries will fail between 16.6 and 21.4 hours

We plug the value of mean and standard deviation

Approximately 99.7 % batteries will fail between 19 - 3*1.2 = 19 - 3.6 =15.4 and 19 + 3*1.2 = 19 + 3.6=22.6

Virtually all failed between 15.4 and 22.6 hours

Answer for C part

Virtually all failed between 15.4 and 22.6 hours

Answers :-

a ) Approximately 68 % batteries will fail between 17.8 and 20.2 hours

b ) Approximately 95 % batteries will fail between 16.6 and 21.4 hours

c ) Virtually all failed between 15.4 and 22.6 hours

Look the image of normal distribution

I hope this will help you :)