Laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation with a mean of 750 hours and a standard deviation of 75 hours. find the probability that a randomly selected light bulb will last between 750 and 825 hours.

The quick way would be to use the 68-95-99.7 rule. Notice that 825 = 750 + 75, so that 825 is one standard deviation away from the mean. The rule says that approximately 68% of a normal distribution lies within one standard deviation of the mean (in the interval [750 - 75, 750 + 75] = [675, 825]), so about 34% would lie within one standard deviation to the right of the mean.

The longer but more accurate way would be to compute the probability:

where is a random variable following the standard normal distribution with mean 0 and standard deviation 1. We find

as expected.