Question 1180992
mean is 221 hours.
standard deviation is 7 hours.


a) What is the probability that a light bulb lasts between 215 and 234 hours?


the probability is .7727, using the calculator that can be found at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>


here's a display of the use of that calculator to solve this problem.


<img src = "http://theo.x10hosting.com/2021/052601.jpg">


b) What is the lifetime of a light bulb that is at the 85th percentile?


the lifetime of a bulb at the 85th percentile is 228.255, using the same calculator as above, only using the value from an area option rather than the area from a value option as was done solving the previous question.


here's a display of the use of that calculator to solve this problem.


<img src = "http://theo.x10hosting.com/2021/052602.jpg">


the 85th percentile means the lifetime of the bulb is greater than 85% of all the bulbs.