00:01
For this question, we are told that aptitude, that scores on an aptitude test, call this random variable x, are normally distributed with a mean of 480 and a standard deviation of 95, and we are asked what is the minimum score needed to be in the top 25 % on the test.
00:20
So if this is the normal distribution representing the scores for this test, we have a mean of 480, standard deviation of 95.
00:29
There exists some score here such that the probability of being bigger than that score is 25 % or 0 .25.
00:45
So graphically, the area under the curve and to the right of the score is equal to 0 .25.
00:56
So this blue shaded region has an area of 0 .25.
01:00
Because the total area under the curve is 1, if the area under the curve to the right of x is 0 .25, then the area under the curve to the left of x is .75.
01:12
So the red shaded region has an area of .75, which means that we can re -express the problem like this...