00:01
So here we're given some information about sodium consumption.
00:03
The average american man consumes 9 .6 grams each day with a standard deviation of 0 .8 grams.
00:08
That's our random variable, right? and it's normally distributed with a mean of 9 .6 because the mean of the normal distribution is what the actual average is in the underlying population, right? so when we say that the average is 9 .6 grams, that is the true population mean around which the normal distribution is centered.
00:28
And then we're told that the standard deviation is 0 .8.
00:31
So i'll go ahead and put 0 .8 in for the standard deviation.
00:34
Now we've got probability to do, right? so for the first real question, we're asked what the probability is that x is between 9 .5 and 10 .1 grams.
00:46
And so there's a few ways to do this.
00:48
I'm going to appeal to microsoft excel because i think it's a common method that many people may have some exposure to, right? when we're talking about statistical questions.
00:58
And to calculate normal probabilities in excel, we appeal to norm .dust, right? and the answer here would be, well, let's think about it.
01:07
If i sketch my normal distribution, right, we're cutting at 10 .1.
01:13
We're cutting at 9 .5, and we're trying to capture this area of the distribution, right, that is centered around mu equals 9 .6.
01:25
So norm .dist says give me the value below a point, in this case 10 .1, if you're in a normal distribution with a mean of 9 .6, a standard deviation of 0 .8.
01:35
And true says give me all the probability to the left.
01:38
So this command here, right, this green one, would give me all the area to the left, all the area to the left.
01:47
But that's too much, right? we only want this area between these points.
01:52
So i need to get rid of this area.
01:55
Here down below.
01:57
To throw away that area, i subtract off the probability mass that is below 9 .5, underneath the normal distribution with a mean of 9 .6 and a standard deviation of 0 .8...