I’m having trouble with area problems that are finding the top _% – help!
ANSWER:
If you like to see first some more step-by-step ones, I just made more examples here.
Here is the explanation for these problems in general and more:
The top _% means we are given a backwards right tail area problem. It could also say find the are with _% of the data to the right of it. Same idea.
Like, find the top 80% would be the same as find the value associated with 80% of the data to the right of it.
We need to eventually get to an x value to answer these problems but in order to get there we will have to have the z-score.
In order to get a z-value we need to look for the closest Left tail area.
So the first step in these problems is finding what left tail area we are given.
–> If we are asked for the top 20% then this is a right tail area of .2 We will have to put this in terms of left tail area = .8. Now we use the table to find the closest area to .8 and write down that z-score. Once we have the z-score we use that formula plugging in what we have to find the associated x-value.
- In the More Examples w/Normal Distribution! mini-lecture a simplified version is For a standard normal curve find the z-value with 80% of the data to the right of it.
- In Applications of the Normal Curve (Standardizing) we do What about 80% of this data above or to the right? Can you figure out this x-value?
- Midterm Review Practice Above what value would expect to find the top 25% of the IQ scores?
From the Applications of the Normal Curve mini-lecture:
Sometimes you would like to start with an area you are interested in and go in the other direction. That is you start with a percentage of the data you are interested in then go and lookup the z-value that corresponds to this area. From the z-value you can then work your way back to the x-value. This kind of problem looks like this:
Backwards normal curve problems: area –> z-value –> x-value
Further help if you are confused what to do once you do the initial step of getting the right tail area, the top _% expressed in left tail area: