Understanding normal approximation to binomial requires examining multiple perspectives and considerations. statistics - Why normal approximation to binomial distribution uses np .... I was reading about normal approximation to binomial distribution and I dunno how it works for cases when you say for example p is equal to 0.3 where p is probability of success. Normal approximations of Binomial distributions. In this context, why do we adjust by 0.
Similarly, i'm reading about binomial distributions and I found this problem: We're trying to find the probability of finding 70-245 successes, given a population of 245 and a probability of success of 25%. probability - When to use the continuity correction for normal .... Another key aspect involves, it is always a good idea to use a continuity correction when approximating binomial probabilities by normal ones. // There is a big difference between (b) in your original question and (b) in the somewhat smudgy photograph.
In the second version of (b), $32 \times 36 = 1152$ raisins--almost half of the 2500 available raisins. probability - How to prove that the binomial distribution is .... The Wikipedia Page has a good explanation and also have a look at the figure for CDF and the PDF which will give you some insight. Apart from that, the proof is actually (as an answer states) due to De Moivre. One thing to keep in mind is that the Binomial can also be approximated to a Poisson with a subtle difference in condition.
Conditions for Normal Approximation to Binomial. That said, you are probably asking for a better approximation to the binomial distribution in the sense of having more higher-order terms. I don't know whether the tail bounds on Wikipedia would help you, since I'm not familiar with them. Conditions needed to approximate a Binomial distribution using a Normal ....
Three further comments on normal approximation to the binomial are also relevant. (a) It is important to use the continuity correction unless n n is several hundred. (b) A Poisson approximation is often better than a normal approximation, especially if n n is large and p p is small. (c) Nowadays, modern software (R, SAS, Minitab, MatLab, etc.) provides the opportunity to get exact binomial ... In this context, statistics - Why are -/+0.5 scale divisions used in continuity ....
Why are half-scale divisions used in continuity corrections for binomial approx to normal distribution? Why specifically half and not another correction? probability - Approximation with a normal distribution - Mathematics .... You can use a normal approximation with her $\mu$ and $\sigma$ in the R statement 1 - pnorm(99.5, 125, 13.693) to get $0.9687,$ rounded to four places. Ordinarily, you cannot depend on more than about two decimal places of accuracy form a normal approximation to the binomial or negative binomial distribution.
Using Normal and Binomial approximations for airline tickets. If the airline sells 185 tickets for a flight with only 180 seats, use the normal approximation to the binomial distribution to find the probability that a seat will be available for every person holding a reservation and planning to fly. (Round your answer to four decimal places.) I am frustrated at this problem.
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