00:01
We're told that a manufacturer knows that their items have lengths that are skewed to the right with a mean of 15 .4 inches.
00:11
So i'm just going to write down all the important information here from the question.
00:14
Mean is 15 .4, a standard deviation of 2 .3 inches, and if we're going to just choose 48 items at random, what is the probability that their mean lengths are greater than 15 .8 inches? so we want to find the probability that the sample mean is greater than 15 .8.
00:55
So let's go ahead and change this into a z -score because our sample size is 48 items, so that's going to be larger than 30, so we can do z.
01:06
So let's just actually find z first.
01:08
Z is equal to x minus the mean divided by sigma over square root of n.
01:25
So that's going to be 15 .8 minus 15 .4 divided by 2 .3 over square root of 48.
01:47
And now we're just going to plug this into our calculator.
01:52
And when you type this in, let's see, you want to round to the nearest hundredth place because that's where most z -scores are rounded to.
01:59
So i get a z of about 1 .20.
02:04
So what i did is i changed this probability into just terms of a z so it's easier to find.
02:14
So now i'm finding the probability that z is greater than 1 .2.
02:25
Now to get this answer, you can use your calculator or you can use a z chart or sometimes i'll just google like a simple z -score calculator.
02:35
So what we want to do is go from a z -score to a p -value.
02:41
So it'll take our z -score and it will give us our probability.
02:45
So we're just going to put in our z -score of 1 .2 and it's going to be one -tailed because we're not doing equals not equals, we're just doing greater than.
02:55
And we get a p -value of 0 .1151.
03:01
Let me write that down real quick.
03:04
0 .1151.
03:09
Most probabilities we kind of just round to four decimal places.
03:12
Now that's not going to be our final answer and let me explain why.
03:15
Because when you look at a z -chart, here is our z -score 1 .2.
03:28
Z -charts or z -calculators, whatever it is, they give the area to the left.
03:35
And what does that represent? that represents the probability that we're going to have a z -score less than 1 .2...
