Calculations related to the normal distribution on a Casio 9750 graphing calculator (amzn.to/1AVxr78).
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Approximate script:
I'm going to cover 4 normal distribution problems using a Casio 9750 graphing calculator. Healthy golden retriever weights approximately follow a normal distribution with a mean of 65 pounds and a standard deviation of 8 pounds. The first three questions focus on finding areas under the normal curve, and the last is about finding a golden retriever weight for a particular percentile. Jump ahead to any example using the times shown here.
1. Of healthy golden retrievers, what fraction weigh less than 60 pounds?
To find this answer, we'll start by drawing a plot and finding the Z score. The Z score can be computed by taking the cutoff for the area, which in this case is 60 pounds, subtracting the mean, and then dividing by the standard deviation. So 60 minus 65 divided by 8, which comes out to be Z = -0.625.
To find the tail area, I'll first go to the Stat section by hitting Menu and then navigating over to Stat. Since I want to find something related to the normal distribution, I hit F5 for Distributions, then F1 for normal distribution. Next, I choose F2 for Normal cumulative distribution since I want to find an area. If needed, adjust the settings to punch in variables rather than using a list of data using the F2 button. Here, my calculator is already set on variables. Next, I need to enter a lower bound... however, I want negative infinity! I'll come back to this again in a little bit, but for now I'll punch in a very negative number: -1e99, which is basically an extremely negative number. Next I enter the Z score for the upper bound, which is -0.625. Then I want to make sure I'm using a standard normal distribution: the standard deviation should be 1 and the mean should be 0.
Alright, so I've got my lower bound, my upper bound Z score, and I'm using a standard normal distribution, which means a standard deviation of 1 and a mean of 0. I can hit execute to get the result: about 0.2660.
Alright, now I mentioned that I wanted to come back to that lower bound, since it's a bit obnoxious to have to punch in. Instead, it's actually okay to use -10 instead, since almost all of the standard normal distribution's area is above -10. So if I do the calculation again using -10, I get the exact same result.
Something else you might be wondering about it, why didn't I just punch in the the mean and standard deviation from the problem? If I had, I could have just entered 60 for the upper bound. There are 2 good reasons:
First, if you are learning this as part of a class or for the AP Statistics exam, you need to compute the Z score to show work, so you might as well use it in the calculator as well.
Second, it would be a little trickier to know what I should have put for the lower bound, unless I wanted to punch in that -1e99 number. While in this case, -10 would have been fine, in some other cases it wouldn't have been.
2. Of healthy golden retrievers, what fraction weigh more than 75 pounds?
I'm looking for the upper tail and I again compute a Z score for the cutoff, which in this case is 75 minus 65 divided by 8, which is Z = 1.25. I should also be sure to draw a picture for this situation.
To find the area using the Casio calculator, I can again punch in proper lower and upper bounds for the standard normal distribution. The lower bound is now 1.25, and like how I could punch in -10 for the lower bound, I can use 10 for the upper bound. This gives me an answer of 0.1056.
3. What fraction of healthy golden retrievers weigh between 60 pounds and 75 pounds?
I've already computed the Z scores from the earlier problems, so I can just reuse these. The lower Z score is -0.625 and the upper Z score is 1.25. As before, I should draw a picture showing the area I'm interested in.
I can punch this into the calculator using -0.625 as the lower bound and 1.25 as the upper bound. This gives a fraction of 0.6284.
You might also notice that this middle area could have been computed by taking the area under the normal curve and subtracting out the areas I previously calculated.
4. I want to figure out the weight of a healthy golden retriever at the 80th percentile?
First I'm going to draw a picture, next I'll determine a Z score for the 80th percentile, and finally I'll compute the golden retriever weight for the Z score.
See the remainder of this script at
docs.google.co...
10 сен 2024
