00:01
So we're doing normal distributions.
00:02
In the first one we have a mean of 46 with a standard deviation of 4 squared, which is basically just 16.
00:10
And to get all these probabilities, you need to find the z -scores.
00:13
So let's go ahead and find the z -scores for 56, 49 .2, 40, and 44 .8 by using the formula the data point minus the mean over the standard deviation.
00:25
So i'm gonna find my calculator here, and we'll go 56 minus 46 is 10.
00:31
We'll put that over 16.
00:34
That's gonna be 0 .625.
00:36
We'll put 0 .63.
00:38
49 .2 minus 46, divide that by 16.
00:43
That's gonna be 0 .2.
00:45
We're gonna have this one to be negative 6 divided by 16, which would be point negative 0 .38.
00:53
And then the last one we're gonna have 44 .8 minus 46, and divide that by 16.
01:01
We're gonna get negative 0 .08.
01:05
So that's gonna be the z -scores.
01:07
So we want the probability then that z is less than or equal to 0 .63.
01:14
Probability that z is greater than 0 .2.
01:19
We want the probability that z is greater than negative 0 .38, and we need the probability that z is less than 0 .08.
01:32
That's negative.
01:33
And to do that, you simply go to a z table.
01:35
Before i do that, let's go and get the second one.
01:38
It's the same thing.
01:39
We're just using a mean of 61 and a standard deviation of 12.
01:44
So we're going to get the values for 62 .2, 50 .2, 41 .8, 56 .2, and 73.
01:55
So let's get that real quick.
01:56
62 .2 minus 61, and divide that by 12.
02:00
That's gonna be 0 .1.
02:02
So we're gonna look at z is less than or equal to 0 .1.
02:08
Let's get 0 .2.
02:10
50 .2 minus 61, divide that by 12.
02:15
We get negative 0 .9, and that's a less than as well...