00:01
For this question, we want to give the z score for each test score for two different tests.
00:09
So let's start with part a.
00:13
So for part a, we have a score, which i'll label by x of 92.
00:21
The mean is 78, and the standard deviation is 12.
00:29
Now to calculate the z score, let's just recall how that's done.
00:32
The z score is given by this formula, z equals x minus mu divided by sigma.
00:40
And this is telling you how many standard deviations you are away from the mean.
00:47
So if you get a z score of 1, you are plus 1 standard deviations away from the mean.
00:52
So for this one, our z score will be 92 minus 78 over 12.
01:03
So i will just plug this into a calculator.
01:07
92 minus 78 divided by 12 to 4, 2 decimal places, sorry, that is 1 .17 to 2 decimal places.
01:22
That is our z score for part a.
01:25
Now let's look at part b.
01:28
For part b, our score is 75.
01:32
Our mean is 60 and our standard deviation is 6.
01:43
So let's calculate our z score just as we did before...