Thanks Willba99! How do you do that though? Can you tell me step by step?
Sure! Just for clarification, I'm on a CASIO classpad
So you're looking for Pr(X=1)+Pr(X=0)>.05
What I do is i go to interactive>distribution>discrete>binomialPDF, then enter x=0, Numtrial=x, and pos=.2. When you click okay, it'll say wrong argument type or something. Thats fine just ignore that. Then, in the same row, click + then repeat the process, except make x=1. When you click okay, it'll say wrong argument type again.
I know that sounds confusing when its typed out but its only a few clicks. You should end up with:
binomialPDF(1,x,0.2)+binomialPDF(0,x,0.2)
Copy that, and got to Graph&Table. Paste the formula. Then, instead of clicking the graph button (the parabola shaped one) click the one next to it. Down the bottom, it should the show the associated probabilities for each value of x (each number of trials). Then, scroll down until you find the value of x where the corresponding probability is less than 0.05. For me, that was 22 trials.
(P.s. I'm only year 12, could be wrong 
)
Nice answer by Willba99!
I'll do a similar thing (for the benefit of those on the CAS ti-nspire):
1) On a calculator page, I'll first define a function (Menu>Actions>Define) as
bi(n) = binomPdf(n,0.2,0) + binomPdf(n,0.2,1)
Note I am definiing a function (doesn't have to be bi, can be anything you want
) bi(n) = Pr(X=0) + Pr(X=1) for p=0.2. Use Menu>Probability>Distributions>Binomial Pdf to avoid typing it out.
2) Open a new List & Spreadsheet page
3) Hit ctrl + T
4) Select
bi (or whatever you've defined your function as) from the dropdown list
5) The first column list the values of n, the second column lists the probability Pr(X=0) + Pr(X=1) for that value of n.
We want Pr(X=0) + Pr(X=1) < 0.05, so scroll down the second column until the number is < 0.05. Like Willba99 has said above, the lowest value for n for which the probability is < 0.05 is 22.
For this http://imgur.com/a/ok4jm
Apparently option A is not correct. But isn't I and II both true? The answer says I is not. So the answer is C?
Thank you
I would agree with you - a higher level of confidence (e.g. 99%) would require a wider confidence interval than say, a 90% level of confidence. I feel that the textbook may have made a mistake here, unless we're both missing something. Perhaps someone else has some further insight?
EDIT: Perhaps, option I is incorrect since it's not 'strictly' always true? Consider a 99% CI with a very large sample size, versus a 95% CI with a very small sample size. In this case, the 95% CI interval (with lower confidence) would have a wider confidence interval, due to the effect of sample size. The question doesn't really state whether the standard deviations or sample sizes remain constant, so this is the only reason I can think of.
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