Although the Binomial Distribution Is Discrete, in Many Cases It

Multiple Choice

Although the binomial distribution is discrete, in many cases it can be modeled using a normal distribution.If X is binomial with mean = μx and standard deviation = σx, then we can define a new random variable Y that is normal with the same mean and same standard deviation.In this case under certain assumptions,P(X ≤ x) ≈ P(Y ≤ x) .This relationship is most useful when X has a large number of trials.If X is binomial with a mean of 25 and a standard deviation of 4.33 (n = 100, p = 0.25) , what is P(X ≤ 23) using the normal approximation discussed here?

A) 0.3228
B) 0.4300
C) 0.4500
D) 0.6772