00:01
This problem tells us that the gmat is a standardized test used by many universities, and it says that the average gmat score is 547, so the mean is 547, with a standard deviation of 100.
00:17
It said to assume that gmat scores are normally distributed or bell -shaped, and we need to find four different things here.
00:23
So let's begin with part a, where we're asked to find the percentage of gmat scores that are 647 or higher.
00:31
So here we're finding the probability of x being greater than or equal to 647.
00:37
So the first thing we need to do is to find a z score for 647 using this red equation i have on the screen.
00:45
So using the equation, we'll have z is equal to x, which is 647, minus the mean, which is 547, divided by the standard deviation, which is 100.
00:57
When you calculate that, you should get a z score of 1 .00.
01:02
Now that we have our z score for 647, let's turn to our z table on the left side of the screen and find our z score.
01:09
So we'll go down on the left -hand side to 1 .0, which is right here, over on the right to 0 .00, and if we meet in the middle, we get 0 .8413.
01:21
Now our z table always gives us what is less than what we're trying to find.
01:25
So this probability here that we just found is the probability of x being less than 647.
01:31
But we want the probability of x being greater than or equal to 647.
01:36
So to find what's greater than, we'll have to subtract what's less than from 1.
01:40
So if we take 1 minus 0 .843, we'll get our answer, which comes out to 0 .1587.
01:48
And the problem asks for percentage, so as a percentage, this would simply be 15 .87%.
01:58
Now in part b, we're asked to find the percentage of gmat scores that are 747.
02:03
So now we're finding the probability of x being greater than are equal to 747.
02:09
So we'll do the same thing we did in part a by finding a z score using the same equation, but this time x will be 747.
02:18
We again subtract the mean and divide by the standard deviation, and that gives us 2 .00 as our z score.
02:26
If we find that in our table 2 .00, we get 0 .9, 972.
02:35
And again, as in part a, this is the probability of x being less than 400, or excuse me, 747.
02:42
So we'll have to take one minus this to get the probability of it being greater than or equal to.
02:49
And that'll give us 0 .028 or 2 .28%.
02:55
Moving on now to part c, where we're asked to find the percentage of scores between 447 and 500...