00:02
Scores on a test are normally distributed with a mean of 65 and a standard deviation.
00:09
What percentage of the scores are less than 54? so to calculate that, we're going to need to get a z score for 54.
00:23
So we're going to do 54 minus the mean divided by the standard deviation, which will actually be negative 11 divided by 9, which is negative 1 .22.
00:41
And now we're going to reference the standard normal probability table.
00:46
Look up a z score of negative 1 .22, which corresponds to a probability of 0 .1112.
00:56
And that will be the answer for less than 54.
01:02
So on my bell curve here at 54, the area to the left is 0 .111.
01:11
Now the next question we want at least, in 80.
01:14
So now a z score for 80 is going to be 80 minus 65 divided by the mean, which will be 15 divided by 9, which is 1 .67.
01:27
So we'll look up a z score of 1 .67, which corresponds to a probability to the left of 4 .9525.
01:41
So here's what i mean at 80.
01:43
I'll do this in blue.
01:46
At 80, the probability to the left of that z score is 0 .95.
01:55
So all the way to the left is 0 .9525.
01:59
But we want at least in 80, so we want this part of the bell curve down here...