Suppose X is a binomial random variable with n=100 and p=0.3. Estimate P(X=40) by using the normal approximation.
Added by Jeffrey B.
Step 1
The mean of a binomial distribution is given by μ = np, where n is the number of trials and p is the probability of success in each trial. In this case, n = 100 and p = 0.3, so μ = 100 x 0.3 = 30. The standard deviation of a binomial distribution is given by σ = Show more…
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'Suppose X is a binomial random variable with n=100 and p=0.3. Estimate P(X-40) by using the normal approximation'
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Compute $P(x)$ using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so, approximate $P(x)$ and compare the result to the exact probability. $$n=40, p=0.25, X=30$$
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