I got a stat test tomorrow and cant remember how to do this one problem any help would be great.
Here is the problem
If the average life of Die hard batteries is 80 months with a standered devaition of 20 months. Find the time that seperates the top 25% of batteries that last longer then the rest.
Let X be the random variable you’re dealing with, in this case the life of a randomly selected battery. Transform this to the standard normal by subtracting the mean and dividing by the standard deviation ( take care here: in an exam they will often give you the variance). Here, Z = (X - 80)/20.
Now you need the statistics tables. We want the time corresponding to the top 25%; this is the same as the bottom 75%, so look for the z-value corresponding to a probability of 0.75.
Now, z = 0.67 gives 0.7486 and z = 0.68 gives 0.7517; so z = 0.675 will give us roughly 0.75 ( you can make this more accurate by using linear interpolation, if you want). So
(Z - 80)/20 = 0.675
Solving for Z, we get a time of 93.5 months.