Normal Distributions

Example :
An average life of 750 hours is printed on the side of a box of 75 watt light bulbs. If the lives of the light bulbs are normally distributed with a standard deviation of 22 hours, what percent of the bulbs will last between 730 and 780 hours? At least 785 hours? Less than 715 hours? If the company is only prepared to replace 15% of their guaranteed light bulbs, how many hours should they guarantee?

Solution :
To find the area (percent) between 730 and 780 under the normal curve with mean 750 and standard deviation 22, we can use the normal distribution probability. From the statistical data list, press "F6" (DIST), then press "F1" (NORM), and then press "F2" (Ncd). Enter the lower boundary, upper boundary, and standard deviation, and mean. Press "F1" (CALC) to get the area between

To get the area more than 785, you need to change the lower boundary to 785 and the upper boundary to infinity. Press "F1" (CALC) to get the area.

To get the area less than 715, change the lower boundary to negative infinity, and upper boundary to 715. Press "F1" (CALC) to get the area.

To get the number of hours, you need to use inverse cumulative normal distribution. Press "F3" (InvN) from the normal distribution menu. Enter the area (probability value), standard deviation, and mean. Press "F1" to get the number of hours.

Therefore, about 73% of the bulbs will last between 730 and 780 hours, about 5.6% of the bulbs will last at least 785 hours, about 5.6% of the light bulbs will last less than 715 hours, and the company should guarantee that their light bulbs will last at least 727 hours.