A binomial distribution has 50 trials (n = 50) with a probability of success of 0.50 ($\pi$=0.50). We would like to find the probability of 34 or more successes using the normal distribution to approximate the binomial. Applying the continuity correction factor, what z-score should be used?
A) 2.404
B) 2.546
C) 2.687
D) 0.50

Question

Quizplus · Accepted Answer

To approximate the binomial distribution using the normal distribution, apply the continuity correction factor. For 34 or more successes, use 33.5 as the cutoff. The mean is $n\pi = 25$ and the standard deviation is $\sqrt{n\pi(1-\pi)} = 3.54$. The z-score is $(33.5 - 25) / 3.54 = 2.404$.

A Binomial Distribution Has 50 Trials (N = 50) with a Probability