00:01
The question says that assuming the heights of college women are normally distributed with mean 61 inches and standard deviation 3 .4 inches, answer the following four questions.
00:13
So our first question here, letter a, asks what percentage of women are taller than 61 inches? so we're finding x greater than 61.
00:26
So first, let's write down what the problem gives us.
00:29
So they give us the mean, which is 61, and they give us the standard deviation, which is 3 .4.
00:39
So for a, we'll have to find the z score for 61.
00:43
So we'll use this red equation i have here.
00:47
So z equals x, which is 61, minus the mean, which is also 61, divided by the standard deviation, which is 3 .4.
00:59
Now we can already see without completely calculating this, that this is going to come out to 0 .0.
01:04
Because any fraction with zero on the top is zero.
01:09
So we get zero for our z score.
01:12
And then if we look that up in our table over here, zero right there is equal to 0 .5.
01:26
The problem asks for what percentage of women are taller than 61 inches, and we know that z scores always tell us what is less than or to the left on the standard normal curve.
01:38
So we would have to subtract 0 .5 from 1 to get the correct answer, but in this case, it doesn't matter, since we're going to get 0 .5 anyway, subtract it from 1.
01:50
And it asks for the answer to be in percentage form.
01:55
So we'll move the decimal place, two places to the right, and we'll get 50%.
02:01
This makes sense that it would be 50%, because the mean is 61, and letter a is asking about 61.
02:10
So whatever the mean is, 50 % are before the mean, are after the mean.
02:16
So it makes sense that we could 50 % for our answer.
02:19
Now for letter b, letter b says what percentage of women are shorter than 61 inches? so this time we're finding it's less than 61.
02:29
Now we could write out the same thing that we did above, but we're going to get the same answer.
02:34
We're going to write in the same equation.
02:37
We're going to get zero, look it up in the table as we did, and we'll still get 50%.
02:41
So we know that the answer for b is going to be 50%.
02:46
Because as i said, there's 50 % before the mean and 50 % after the mean.
02:52
Letter c will be a little more involved.
02:55
Letter c asks what percentage of women are between 57 .6 inches and 64 .4 inches.
03:02
So this is asking us to find what is greater than 57 .6 and less than 64 .4...