00:01
For this exercise, we are told that the length of time to perform a certain type of surgery, we'll call that random variable x, is normally distributed with the mean of 132 .4 minutes and a standard deviation of 15 .7 minutes.
00:17
And we were asked, what is the minimum surgery length required to be considered to be in the longest 4 % of surgeries? so mathematically, there is some length.
00:34
Such that the probability of being at least that long is 4%.
00:44
Graphically, if this is our normal distribution, the mean is at 132 .4, there is some surgery length, such that the area to the right of it, or the probability of being greater than it, is 4%.
01:08
Since the area under the curve for any probability distribution is total is 1, i can also say that the area to the left of x is .96.
01:28
So this means that the probability of being less than x is 0 .96...