Assume the mean useful life of a particular light bulb is 2,000 hours, which is normally distributed with a

standard deviation of 300 hours. What is the range of the useful life of light bulbs within two standard

deviations of the mean?

Mean Usual Life of bulbs = x = 2000 hours

Standard Deviation = s = 300 hours

The data within 2 standard deviations about the mean is considered as the usual values. The data far from the 2 standard deviations is said to be unusual.

So the range of usual values can be expressed mathematically as:

x - 2s to x + 2s

Using the values, we get:

x - 2s = 2000 - 2 (300) = 1400

x + 2s = 2000 + 2 (300) = 2600

This means, a bulb with a useful life in between 1400 hours and 2600 hours will be considered as usual. Thus, the range of the useful life of light bulbs within two standard deviations of the mean is 1400 to 2600 hours.