Question

The amount of time a certain brand of light bulb lasts is normally distributedwith a mean of 1200 hours and a standard deviation of 100 hours. Using theempirical rule, what percentage of light bulbs last between 1100 hours and1300 hours?

Answer 1

According to the Empirical Rule 67-95-99.7, for a given spread of normally distributed data, 67% of the data points lie within 1 standard deviation from the mean value, 95% of the data points lie within 2 standard deviation from the mean value, 99.7% of the data points lie within 3 standard deviation from the mean value

According to the given problem, the mean is 1200 hours and the standard deviation is 100 hours. Then using the Empirical Rule, it follows that,

$\begin{gathered} P(1200\pm100)=67\text{ percent} \\ P(1100\text{ }to\text{ }1300)=67\text{ percent} \end{gathered}$

Thus, 67% of the light bulbs last between 1100 hours and 1300 hours.