00:01
So we're told that the birth weights of full -term babies in the u .s.
00:04
Approximately following normal distribution with a mean of 3 ,485 and standard deviation of 425 grams.
00:21
So the question is, well, what proportion of these full -term babies weigh between 2 ,800 grams and 3 ,000? 600 grams.
00:34
So in order to find this, we're going to look at a bunch of z scores.
00:38
So let's think about it first in terms of like what this looks like visually.
00:43
Here's our mean.
00:46
And that's, again, 3 ,485.
00:51
And we're trying to find where 2 ,800 is, which will be somewhere over here, 2 ,800.
01:01
And then 3 ,600, which will be somewhere over here.
01:07
What we're looking for is this area in between them.
01:12
Now, when we look up our z scores, it's going to be helpful when we go to the z table because it'll tell us like the proportion underneath that this, the normal curve, how much it's going to actually like the z value is going to be worth.
01:29
So for $2 ,800, it'll give us this amount here, like kind of that red amount.
01:33
For 3 ,600, it's going to give us this entire amount, this entire, all the green and all the red.
01:42
So it'll help us because we can then cut out this overlap.
01:49
And all that will be left is that green shaded area, which will tell us the proportion we're looking for.
01:55
So let's jump right to it.
01:57
We have two z values that we need to find here...