00:01
This problem tells us that the average american man consumes 9 .5 grams of sodium each day.
00:07
It says that the sodium consumption of american men is normally distributed with a standard deviation of 0 .9 grams.
00:13
We're supposed to assume that a american man is chosen at random, and we're supposed to let x be equal to the amount of sodium he consumes.
00:23
So first, let's jot down what we were given here.
00:26
We were given the mean, which is 9 .5, as well as the standard deviation, which is 0 .9.
00:32
Those will be important for us to answer the next three questions in this problem.
00:36
So we'll start off with part a, which says what is the distribution of x? so that is n, because it's a normal standard distribution.
00:45
Then we put a parentheses and the mean always comes first, which was given to us as 9 .5, and then the standard deviation, which was given to us as 0 .9.
00:54
So this is our distribution here for this problem.
00:58
Now in part b, we're asked to find the probability, that a randomly selected american man will consume between 10 .5 and 11 .2 grams of sodium.
01:08
So we're finding the probability that x is greater than 10 .4 but less than 11 .2.
01:15
So the first thing we need to do here is to find z scores for both 11 .2 and 10 .4 using this red equation i have on the screen.
01:24
So we'll start with 11 .2.
01:26
Z is equal to x which is 11 .2, minus the mean which was given to us as 9 .5, and divided by standard deviation, which was also given to us .9.
01:36
If you calculate that, you get 1 .89 as our z score.
01:41
Now let's do the same thing for 10 .4.
01:44
So now 10 .4 will be x, minus the mean divided by standard deviation, and that gives us 1 as our z score.
01:53
So now we need to go over to our z tables here on the left side of the screen and locate our 2 z scores.
01:59
So we'll start with 1 .89.
02:01
So we'll go down on the left hand side to 1 .8, over on the right to 0 .09, and we get .9706.
02:11
Now we'll do the same for 1, so 1 .00 will give us 0 .8413.
02:20
Now our z table always gives us what is less than what we're trying to find.
02:25
So here this probability is what is less than 10 .4, and this probability is what is less than 11 .2.
02:32
But we want to find what's between 10 .4 and 11 .2.
02:36
So to do that, we'll have to subtract our lesser value from our greater value.
02:40
So we'll take 0 .9706 minus 0 .8413, and that'll give us what is between those two points, which is going to be 0 .19, or excuse me, 1 ,293.
02:54
So this is our probability for part b...