I've heard that when n is great enough a value, the sum of all values from binompdf within a bound can be approximated with normalcdf.

I wasn't paying enough during Stat yesterday, obviously (someone asked me to make a game on their calculator… I'm guilty), and now I don't understand the homework.

I understand how to use binompdf, but not binomcdf, and not how to approximate it with normalcdf…

Ex: Suppose that James guesses on each question of a 50 question true/false quiz. Find the probability that James passes if… passing is 25+ correct questions… passing is 30+ correct questions… and passing is 32+correct questions.

I eventually got the answers by using sum() and seq() in conjunction with binompdf(), but I'm positive that there's a simpler way to solve these problems using the other commands. I would know if I had paid attention in class yesterday, sorry.

Help, please?

This might prove useful.

Just to refresh my memory…

By summing the values of the binomial pdf, you get the binomial cdf (PDF = Probability Distribution Function, CDF= Cumulative Distribution Function). The binomial PDF given probability P, with N trials and K successes is given by :

(So p^{k} gives number of successes, (1-p)^{n-k} gives number of failures, the n choose k gives the number of ways this can be done).

Luckily, for p=.5, this becomes:

(2)And the problem of summing becomes easier (but still impossible to find an explicit form fort the partial sum):

(3)In this case, though, we know that the sum of all nCk on a row is 2^{n}, so the solution to the first part is:

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Thanks. Can you explain how something that is

B(n,p)

is

N(np,sqrt(np(1-p))) - (we use the standard deviation rather than the variance as the second argument in our class, unlike wikipedia)

?

I understand how the mean = np, but I don't understand the formula for the standard deviation.

I was worried I would have to try to type out the proof, but luckily I found a nicely done one here. I am not sure what level stats class you are in, though. I taught myself statistics for the AP exam and I learned bio-stats which, from what I hear is on par with most other statistics courses. However, mathematical statistics is by far much better, but more complicated. That was where I was first introduced to the notations used in that proof.

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