00:01
We're looking at a normal distribution here.
00:04
It's the distribution of the distance with balls the hip in the outfield.
00:10
So let's draw back.
00:12
So we have a normal distribution.
00:16
The mean, mu, is 259 feet.
00:21
Standard deviation sigma is 37.
00:23
So our first question is, what is the distribution here? so x is in a normal distribution.
00:32
And all you do here is you put the mean first, standard deviation second, like that.
00:40
Part b, we want the probability that a randomly hit ball travels less than 252 feet.
00:47
So 252 is just below the mean, not very far below the mean.
00:51
We want everything less than, so everything to the left.
00:55
So we need to find this area under the curve.
00:58
How do we do that? well, we can't use raw data, we have to convert this into a z -score.
01:03
So z equals x minus mu over sigma.
01:10
So the z score here is 252 minus 259 divided by 37, so that's minus 7 over 37, which is approximately 0.
01:26
0 .189.
01:29
But i am going to hold on to this exact fraction because we're about to do something with it.
01:34
So we've got a z score, this is a measure of how many standard deviations away from the mean a value is.
01:41
And now we need to turn it into a probability.
01:44
If you look at a z score table, you'll be limited to only two decimal places, so it will be an approximation, and it will give you the distance to the mean, and you just take that away from 0 .5 to get the green area.
01:54
If you look at a cumulative table, it will just give you the answer immediately, because it always gives you the area to the left...