00:01
All right, in this question, you're dealing with the normal distribution, and we're talking about miles driven for a car.
00:06
You're given that the mean number of miles driven is 12 ,456, with a standard deviation of 1 ,322.
00:16
What i like to do in a question like this is to definitely draw a sketch to represent my normal model.
00:27
So that represents my normal curve.
00:29
The mean 12 ,456 goes in the center.
00:36
And what we're looking for is the probability of being greater than 16 ,000 miles for a randomly selected car.
00:45
16 ,000 miles is to the right.
00:48
I want the area under the curve to the right of that value, which would represent the probability.
00:56
Okay, so how do we do that? well, we calculate what's called a z score for 16 ,000.
01:04
So 16 ,000 minus the mean 12 ,456.
01:10
And we divide it by a standard deviation of 1 ,322.
01:17
All a z score is is that tells you how many standard deviations you are away from the mean.
01:25
So let me type that into the calculator, 16 ,000 minus 12 ,456.
01:37
Divide that by 1 ,322, and i get a z score of approximately 2 .68.
01:47
Now, a lot of times what we'll use is a z table to help us make that calculation.
01:57
Hold on one second, i didn't want to put it right over that.
02:01
There we go.
02:03
Okay, so this is a z table.
02:05
And we found our z value to be 2 .68.
02:09
So i'm going to find 2 .68 and kind of connect the column in the row.
02:21
And i'm getting a .9963.
02:27
0 .9963.
02:28
That's the area to the left of the z score, 0 .9963...