Question

The batteries from a certain manufacturer have a mean lifetime of 850 hours, with a standard deviation of 90 hours. Assuming that the lifetimes are normally distributed, complete the following statements. 

(a) Approximately _______ of the batteries have lifetimes between 760 hours and 940 hours.

(b) Approximately 95% of the batteries have lifetimes between _______  hours and _______  hours.

Answer 1

According to empirical rule, 68%, 95% and 99.7% values are within 1, 2 and 3 standard deviations of mean.

a) Mean = 850 hours

Standard deviation = 90 hours

760 is one standard deviation below mean and 940 is one standard deviation above mean. Therefore,

approximately 68% of the batteries have lifetimes between 760 hours and 940 hours.

b) 850 - 2x90 = 670

850 + 2x90 = 1030

Approximately 95% of the batteries have lifetimes between 670 hours and 1030 hours.