00:01
For these problems, we're going to be looking at probabilities.
00:04
So for the first one, oh, yeah, for all of these problems before i start, we're going to be using the z score formula, so it's x minus our population mean over our standard deviation.
00:16
So now let's get into the first one.
00:18
Our population mean is equal to six, and our standard deviation is equal to five.
00:25
And we're looking for the probability that our value is between z, 0 and 10.
00:32
So the way i do this is first i get the z score.
00:36
Now all of this can be done with technology.
00:38
So i'm going to do this first one, show you all the steps, and then i'll do a couple of them with technology just to show you.
00:43
So to do the one with without technology, first you're going to find the probability that lines up to just 10.
00:51
So, you know, z is less than 10 basically.
00:54
Or not z rather, that our value is less than 10.
01:01
So to do that, we would just do z equals 10 minus six over five.
01:12
And that is going to equal 0 .8.
01:16
And that is going to line up with a p value of 0 .781.
01:25
You find this by looking it up in the z table.
01:28
So you would look up 0 .80 in a z table.
01:32
Give you the p value.
01:34
Then you're going to find, you know, the probability that x is less than zero.
01:39
So that's going to be z equals 0 minus 6 over 5, which will equal negative 1 .2.
01:51
Look that up in a z table, 1 .20 rather.
01:55
And our p is going to equal 0 .1 .150.
02:01
And then from there, we're just going to get the difference.
02:04
So the p that x is between 0 and 10 is going to equal 0 .7881 minus 0 .1150, and that is going to give us 0 .6731.
02:27
And for the other two questions, where you have a range of values.
02:34
We're actually going to go ahead and use technology for this.
02:37
So our mean is equal to six, and our standard deviation is equal to two.
02:43
And once again, we're looking for the probability that our value lies between zero and ten.
02:49
And plugging this into just any graphing calculator, honestly.
02:53
So you plug in that you have a normal.
02:55
So you would plug in, you write normal distribution, and then you would put in the, you would go ahead and you put in the mean, and our mean here was six, and you'd put in the standard deviation, and then it's going to ask you for what values you're looking for, so you're looking for values between, so your lower limit is going to be zero, and you're looking for up to 10.
03:20
So all of this, so our p is going to equal for this one, 0 .9799.
03:30
So for this one, it's 0 .9759...