Casio fx-9750GII - Calculations for the Normal Distribution
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.com/document/d/14...
Пікірлер: 73
How do I type in -1E99?
@OpenIntroOrg
6 жыл бұрын
There's an "EXP" button that you can use for the "E" scientific notation part. So five button presses: -, 1, EXP, 9, 9
@nyneishiavora5659
10 ай бұрын
I have a fx- 9750 giii but I don't have an EXP button! What do I do?? I have a test tomorrow!! @@OpenIntroOrg
@TheAnonymousBratz
9 ай бұрын
I know this is late but for the people that still may be confused try: 1x10^99 for positive infinity and -1x10^99 for negative infinity.
@TheAnonymousBratz
9 ай бұрын
The “x” stands for multiplying :)
just found you, 7 days before the exam, you increased my probability of getting a decent grade!! Thanks!
@arlo4639
6 жыл бұрын
it's been 5 months... how'd you go?
@user-sb6iw8kd6s
2 жыл бұрын
it's been 5 years... how'd you go?
@saulgoodman8461
Жыл бұрын
@@user-sb6iw8kd6s he is living under a bride because he flunked
@user-sb6iw8kd6s
Жыл бұрын
@@saulgoodman8461 lmao, good Name and pfp btw
I'm so lucky I found your videos. Thank you!
when I put it in -1e+99 and press EXE it changes the number to 99 and says I have an error. Also when I put in -10 for the lower value I get different results from you. I put in the same numbers as your demonstration. Is there any reason why the results are different?
Thank you so much !!! It helped . All my friends have fancy calculators and I don’t. But it doesn’t matter which kind of graphing calculator you have
@OpenIntroOrg
6 жыл бұрын
For what it's worth, the Casio calculator is made just as well as the TI calculators and at less than half the price, so you made a good decision not to overspend. :)
Whenever I set my bounds using variables, it always defaults into a decimal. For example: if I set my lower bound to 65.5, it ends up saying my lower bound is 0.92647058, which in turn gives me the wrong probability. Do you know why this is happening?
I still don’t know how you got 71.73
Why did you use the z-score and to use the calculator when you could have just used the values provided in the question straight into the calculator? Did I miss something...
@OpenIntroOrg
5 жыл бұрын
Often times to get full credit for a question in a class, a student has to show the work of calculating the Z-score and use the standard normal distribution, N(0, 1). That is the only reason we did it this way.
I kept getting the wrong answer in class bc I was inputting 10^-99, and it would give me a MA Error if the LB was negative, so using -10 instead saved my grade! Thank you so much!!!
This video saved me so much grief.... Thanks!
Hi 👋Thanks for your explanation please help me with my Casio fx-115ES plus and also I did not understand you how can I find the value with like this great than and less than
I’m not able to punch in 1e+99 and get the correct answer. I have the fx-9750ga PLUS
Great video! Thank you so much for sharing! I am little bit confused on a detail. Why with the normal distribution the mean and standard deviation from the problem are not used? For the Poisson and Bionamial distribution, on this calculator, you input this values.
@OpenIntroOrg
6 жыл бұрын
Hi Wendi, you could use those in the calculator to bypass getting the Z-score. The reason we don't do that is two-fold: 1) Being very familiar and comfortable with Z-scores helps later with hypothesis testing, particularly around Z and T test statistics (if those terms don't make sense yet, don't worry about it!). 2) Because of #1, it's common for teachers to require students to compute the Z-score when working with the normal distribution.
@wen6519
6 жыл бұрын
OpenIntroOrg thank you guys! I ended up using the target statistic as my limit instead of the z score, then using the mean and STD deviation given. I got the same result as with the z core, but I am not sure if this is the right approach?
@OpenIntroOrg
6 жыл бұрын
That approach should give you the same answer :) If you're interested, the following video might be helpful to understand why these approaches work out to be the same: kzread.info/dash/bejne/hZOkl6Zmibuyg5c.html
how did you go from x-65/8=0.8416 to x=71.73?
@OpenIntroOrg
6 жыл бұрын
Starting with: (x - 65) / 8 = 0.8416 Multiply by 8 on each side: 8 * (x - 65) / 8 = 8 * 0.8416 Simplify: x - 65 = 6.7328 Add 65 to each side: x - 65 + 65 = 6.7328 + 65 Simplify: x = 71.7328
Thank you so much for uploading this video, it is very helpful! I didn't get the left and right concept when you were solving the fourth problem. When are you supposed to select left and right?
Oh my god I could hug you for that "-10" trick!
I have the CASIO and am glad I saved money and bought this thing, although my school book only shows the everything else like the TI-84 or excel or minitab, but hey I have internet. I am curious though maybe you can help me. Why does my book talk about the Critical value method? It says this method can be done with technology but does not show us the difference between the P-value method and critical value method with technology. What gives?
@OpenIntroOrg
6 жыл бұрын
For the critical value method when the normal model is appropriate, you'll want to (1) Find the cutoff that where the tail area (or areas if two-sided test) is equal to the significance level, alpha, which is usually 0.05. The cutoff value is called the critical value. For example, for a 2-sided test with alpha = 0.05, the critical value is 1.96 since the sum of both tails (below -1.96 plus area above 1.96) is 0.05. (2) Compute the test statistic, which is typically [point estimate - null value] / SE. (3) If the test statistic (in absolute value) is larger than the critical value, then reject the null hypothesis. This method is consistent with the p-value method (which is more commonly used, especially when using technology), since if the test statistic is larger than the critical value, the tail (representing the p-value) will be smaller than the alpha level. If using the t-distribution (or another distribution in another context), the cutoff will use that distribution rather than the normal distribution.
I calculated the exact same values by punching in the mean and standard deviation. skipping a step with the whole z value calculations, any draw backs to this? Is it possible to get an an answer wrong?
@OpenIntroOrg
5 жыл бұрын
The only drawback that comes to mind is if your instructor or exam requires the Z-score step for showing work. The final answer should be the same in each case.
@viktorneshikj6056
5 жыл бұрын
OpenIntroOrg right that makes sense, and it would also be needed if you need to work out the standard deviation or mean when there is a given x value you would need the z value. Thanks!
What is the function for positive infinity?
The numbers I got had very lengthy decimals places, can I round my answers?
@OpenIntroOrg
5 жыл бұрын
Generally, yes, with how far you can round being potentially dependent on the instructor for a course. Usually 4 decimal places is safe for rounding a final answer for a probability question.
great tutorial thnkx
This was immensely helpful! That's a like from me!
Thank you, such a useful tutorial!
I don't understand what the heck the npd option under normal distribution means or does.
@OpenIntroOrg
3 жыл бұрын
TLDR: You don't need it. Details: "npd" stands for "normal probability density". When we plot the normal distribution, this basically gives the y-values of the distribution curve. It will probably never be useful to you, at least the values that you'd get from a calculator (one at a time). The only time we use it is when we are working in statistical software where it is possible to get a very large number of points along a curve using one line of code, and then we use those to create graphics for education resources. Ultimately, it's just not a useful value function on a calculator.
@HenrikMyrhaug
3 жыл бұрын
@@OpenIntroOrg Thanks, that explains it!
Hey for some reason I keep getting 0 for my probability, do you have any thoughts on how to fix it?
@OpenIntroOrg
5 жыл бұрын
A couple things to try out: - Set the lower bound to -10 and the upper bound to 10. - Confirm the standard deviation is set to 1 and the mean is set to 0. Note that they are listed in this order; if SD = 0 and mean to 1, then it will likely give a zero probability.
@lawrencekungu5164
5 жыл бұрын
OpenIntroOrg thank you so much you just earned yourself a new subscriber 👍🏾
How would you do a Two tailed T-test?
@OpenIntroOrg
9 жыл бұрын
+Salim El-Othman We have a bunch of other videos on how to use this calculator in this playlist: kzread.info/head/PLkIselvEzpM7xx4WIYydlxRFRiA_kPDxf You'll want the one sample and / or two sample hypothesis test videos.
@OpenIntroOrg
8 жыл бұрын
+Luis De León Looking around a little bit, there is some functionality -- e.g. just solved a 3rd degree polynomial to try it out and confirmed the solution -- though haven't dived in much. If you look at time 1:00 in the video, the solver is #8 in the menu.
You're the best!! Thanks! :D
PLease help me! on this video at 1:35 you input a negative infinity , what buttons do you push on the calculator to get that? basically what buttons do I push to get on my screen either -1e+99 or 1e+99. I cannot find it anywhere in the manual. Help!! And with this coronavirus stuff i cannot get a live person with Casio and my teacher uses the TI calculator which is different from the casio....
@ae1ae2
4 жыл бұрын
Browse the other comments. They've already answered this question.
Fantastic! Thanks!
why is 80 percentile refer to 0.8 area
This was a good video thanks!
what did you do to get 71.73 in the last question
@OpenIntroOrg
2 жыл бұрын
After getting the Z-score (0.8416), set up the Z-score formula with `x` as the unknown (mu = 65 and sigma = 8 in this example). Solving for x gives 71.73. For ref, here's a longer form video going over normal distribution calculations in case that's useful: kzread.info/dash/bejne/hZOkl6Zmibuyg5c.html
Thanks that helps me a lot!!!
Thanks dude!!
What should I press for 1e99?
@OpenIntroOrg
6 жыл бұрын
Bridget Sonobe asked a nearly identical question below, and you can find our answer there!
@jazzyjazzlolily
6 жыл бұрын
where
Thanks bro
how did you do the infinity on the calc?
@OpenIntroOrg
8 жыл бұрын
+CloudedTear816 If you want to make a very big negative number, e.g. -1e99, then hit - 1 EXP 9 9, where the EXP button is to the right of the period. This isn't negative infinity, but for these types of exercises, it's close enough. When using a normal distribution with mean 0 and SD of 1, even just -10 is close enough.
@CloudedTear816
8 жыл бұрын
OpenIntroOrg thank you so much! lol wish i knew that for the test two days ago! but i just used 9999999999 and hoped it was right. thank you!
Yooo you had me looking for 10+ minutes for the stupid little E when the while time I could’ve just put a -10? Bruh
@OpenIntroOrg
5 жыл бұрын
The motivation for suggesting the original approach is the case where someone inputs a cutoff value, mean, and standard deviation rather than computing the Z-score (where the mean is then 0 and the standard deviation is then 1). For example, if looking for the upper area where the mean is 5, SD is 10, and the cutoff is 3, then using an upper tail bound of 10 would not work since that is just a Z-score of 1. So if you're standardizing and doing Z-scores, ±10 is fine for getting far out into the tails. If specifying the mean and / or SD (other than mu = 0, sigma = 1), then it's risky.
@XOCash
5 жыл бұрын
OpenIntroOrg well im very appreciative of this video! I feel like im the only one in the school with a casio so nobody else could help, but this will save me, thank you!
Author sounds like Jesse Eissenberg
@OpenIntroOrg
4 жыл бұрын
Or does Jesse Eisenberg sound like the author?
noice ;)