Question

the amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1100 hours and a standard deviation of 70 hours. using the empirical rule, what percentage of light bulbs last between 960 hours and 1240 hours?

Explanation:

Step1: Calculate number of standard - deviations from the mean

First, find how many standard - deviations 960 and 1240 are from the mean.
For \(x = 960\), \(z_1=\frac{960 - 1100}{70}=\frac{- 140}{70}=-2\).
For \(x = 1240\), \(z_2=\frac{1240 - 1100}{70}=\frac{140}{70}=2\).

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that approximately 95% of the data lies within \(z=-2\) and \(z = 2\) standard - deviations of the mean.

Answer:

95%