00:01
This problem tells us that on average american men consume 10 grams of sodium per day.
00:06
So that's our mean.
00:09
It says that sodium consumption of men is normally distributed and that the standard deviation is 8.
00:16
We're asked to find two different things.
00:18
The first thing we're asked to find here in part b is the probability that a randomly selected american man consumes between 11 and 12 .4 grams of sodium per day.
00:29
So in other words, we're finding probability that x is greater than 11, but less than 12 .4.
00:38
So first thing we need to do here is to find a z score for both of these values.
00:42
So we'll start with 12 .4.
00:43
We'll use this red equation i have on the screen.
00:46
So we'll have z is equal to 12 .4, which is x, minus the mean, which was given to us as 10, and divided by standard deviation, which was given to us as 8.
00:56
If you calculate that, you should get a z score of 0 .3.
01:01
Now we'll do the same for 11.
01:03
11 is x minus the mean, divided by standard deviation, gives us a z score of 0 .13.
01:11
So next thing we need to do is to find these z scores in our z table here on the left.
01:16
So we'll go down, for 0 .30, we'll go down to 0 .3 on the left, then over to 0 .00 on the right, and we get 0 .6179.
01:30
Now for 0 .13, we'll get down to 0 .1 and over to 0 .03, and we'll get 0 .5517.
01:44
Now, our z table always gives us what is less than.
01:47
So this value here is what is less than 12 .4.
01:50
This value here is what is less than 11.
01:53
So in order to find what is between 11 and 12 .4, we need to subtract what's less than 11 from what's less than 12 .4...