Casio fx-9750GII - Binomial Formula (Distribution, Including Cumulative Distribution)

Compute a binomial formula (distribution) and binomial cumulative distribution on a Casio 9750 graphing calculator (amzn.to/1AVxr78).
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Approximate script:
I'm going to cover 3 binomial distribution problems using a Casio 9750 graphing calculator. Suppose at a very large college, 30% of students are on the Dean's List. Then suppose I sample 15 college students at random. What is the probability that exactly 5 of the students will be on the Dean's List?
The first problem requires the binomial formula since I want to know what is the probability that exactly 5 of the 15 students will be on the Dean's List. In this example, the number of trials is n = 15, the number of students who satisfy the condition is x = 10, and the probability a random student satisfies the condition is 0.3.
I can compute this result on the Casio calculator by first going to the Stat section using Menu and then hitting 2. Then I can hit F5 for Distributions, F5 again for Binomial distribution, and F1 for Binomial probability distribution. Next, I enter the details into the calculator. Here it's showing the list view, and I'll need to switch to the variable view by hitting F2. Next I can enter x, which is 5, the number of trials, which is 15, and the probability 0.3. Hitting execute gives the binomial probability: 0.2061.
The second question is, what is the probability that fewer than 4 will be on the Dean's List?
I care about the probability that fewer than 4 of the 15 be on the Dean's List. That is, it can be 0, 1, 2, or 3 students. I could compute the binomial probabilities for each of these scenarios and then add them together, but that would take awhile. Instead, I should use the Binomial cumulative distribution function, which gives the left tail of a binomial distribution. To use it, I'll need to again identify our parameters. As before, the number of trials is 15. For a cumulative distribution, I identify the cutoff for the left tail, which in this case is 3, since I'm looking for fewer than 4. Then the probability is the same as before: 0.3.
I'll exit out to the Stat section. As before, I can go into Distribution, then Binomial. To get the Binomial cumulative distribution, I choose F2 for Bcd. Now I can again enter in the context: x is 3, number of trials is 15, and probability is 0.3. Hitting execute gives the answer: 0.2969.
The last question is, what is the probability that 7 or more will be on the Dean's List?
I want to compute the probability that 7 or more of the 15 students will be on the Dean's List. This is the right tail, and while the calculator won't give me a right tail, I can compute the complement, which is the left tail, and then subtract that from 1 to get the right tail. So as before, I determine x, which in this case will be 6, since I want 7 to be included in the upper tail, the number of trials as 15, and the probability as 0.3.
Exiting back to the Binomial cumulative distribution, I can change the 3 to a 6 and hit execute: 0.8689. And again, this is the lower tail. To get the upper tail, I take 1 minus 0.8689, which is 0.1311.
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[@honsbarrera422]

this is awesome, you can also access the binomial probability from the MAT menu (Menu 1) by selecting the [OPTN] ( button right next to the SHIFT button) [F5] for STAT, [F3] DIST, [F5] BINM, there you can select [F1] Bpd or [F2] Bcd or [F3] InvB there you will not see a list like the one from the STATs menu (Menu 2) but you will get something like "BinomialPD(" here you need to type in your digits "BinomialPD(x,n,p) where x=number of trials or people, n=Sample size or total number of people, p=the chance i.e. the percentage or decimal equivalent. notice that in this video the Binomial Probability formula is n first then x, but when entering the data in the BinomialPD bracket it needs to be "x" first then "n" lastly your p.

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[@alana1081]

For the first one, how do you get the result? I’ve tried pressing exe on save res and execute but it doesn’t work

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[@LucasCapochaAlanlz]

please explain how to use the 3er option on the distribution!!!! Thanks

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is there a way to convert the probability from here to a fraction?

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[@greenmelon6387]

How does this work if a number trial isnt given?

[@OpenIntroOrg]

If the number of trials isn't given, it might not be binomial, the information is incomplete, or it may be difficult to identify the number of trials in the context. (Hard to say without more details.) You might also investigate "negative binomial distribution".

[@greenmelon6387]

@@OpenIntroOrg okay thank you.

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[@skidkid5]

i keep using binomial cdf, but it’s giving me p=1 for n=100, x=45, p=.17

[@skidkid5]

idk why its doing that

[@OpenIntroOrg]

The cdf is giving the lower tail of the distribution up to and including x = 45. For the binomial distribution, this is the same as P(x = 0) + P(x = 1) + P(x = 2) + ... + P(x = 45). Because p = 0.17 and n = 100, the mean of the distribution is p * n = 17, and in fact, virtually the entire distribution is less than or equal to x = 45, which is why it is returning a value of p = 1. If you want to get the probability of just x = 45, then use "Bpd". (This will return ≈0.) Hope this helps!

[@ani9514]

what if the q is like this: 4

[@OpenIntroOrg]

Did you mean 2 < x < 4? If so, then first compute the area below 2 and separately compute the area above 4. Then compute 1 minus those two areas will leave you with the area between 2 and 4. For a picture of this sort of situation, see page 135 of OpenIntro Statistics at www.openintro.org/os

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