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[DOC File]AP Statistics
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Aug 27, 2013 · Normal Approximation for Binomial Distributions. Suppose that X has the binomial distribution with n trials and success probability p. When n is large, the distribution of X is approximately Normal with mean and standard deviation. As a rule of thumb, we will use the Normal approximation when n is so large that. np ≥ 10 and n(1 – p) ≥ 10.
normal approximation of a binomial distribution

[DOC File]Basic Counting - University of Kentucky
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In most cases we can improve the situation dramatically by using the normal approximation to the binomial. If n is large enough (we’ve discussed how large on p. 122), then both X and X/n are approximately normal. In particular [(X/n)-p]/( is approximately standard normal since (=p.
normal approximation of binomial rules

[DOC File]STT 315
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The normal approximation of the binomial (below) will be an example. Normal approximation of binomial probabilities for individual x or ranges of x. The expected value for the binomial is np. The sd is root(np(1-p) = root(npq). The normal approximates it using the normal density with mean np and sd root(npq), where q = 1-p.
normal approximation to the binomial equation

[DOC File]MATH 507, LECTURE SIX, FALL 2003 - University of Kentucky
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If X~binomial(n,p), then X is the number of successes in n trials. Define a new random variable . Then is the fraction of successes in n trials. By previous theorems . That is, the mean fraction of successes in n trials is precisely the probability of success on each individual trial, an intuitively reasonable result.
normal approximation to binomial formula

[DOC File]Chapter : The Normal Distribution
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6 The Normal Approximation to the Binomial distribution. 7 The Normal Approximation to the Poisson distribution. 8 When to Use the Different Approximations. 9 When There are More Than One Independent Normal Variables. 10 Miscellaneous Examples ( 1 Introduction. A continuous random variable X having probability density function f(x) where
normal approximation of binomial calculator

[DOCX File]Hyper geometric Probability Distribution
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, identical to the mean and variance of the binomial(n,p) distribution. Similarly, the mean and variance for the approximately normal distribution of the sample proportion are p and (p(1-p)/n). Note: Because the normal approximation is not accurate for small values of n, a good rule of thumb is to use the normal approximation only if np >10 and np
normal approximation example

[DOC File]AP Stats Chapter 8 Notes: The Binomial and Geometric ...
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Continuing with the switches in examples 6 and 7, the count X of bad switches is binomial with n = 10 and p = 0.1. The mean and standard deviation of the binomial distribution are. The Normal Approximation to Binomial Distributions. As the number of trials n gets larger, the binomial distribution gets close to a normal distribution.
binomial approximation formula

Normal approximation of the binomial examples