BINOMIAL, WHY NET CALCULATOR DOESN'T = Z CALCULATION

Question

The STAT TREK online binomial calculator, p = .38, n = 73, prob of 26 or less = .3859.

When I assume binomial = normal, mu = np, sigma = sqrt n*p*(1-p), Z = -.42, prob 26 or less = .3409.

 

All my other examples give Z/online ~.88.

What am I missing?

Thanks;

joe b.

Answer 1

Because binomial is a discrete probability and z-score is based on normal probability which is continuous, they don't operate exactly the same.  The binomial calculator calculated the probability by adding up the probability of exactly 26 plus the probability of exactly 25 plus ... the probability of 0 successes.  A normal probability simply approximates this, but because it is continuous, it allows for 25.34 successes etc.  The normal approximation of binomial distribution is similar in many cases but will never be exactly the same.