Question

for the binomial distribution, which formula finds the standard deviation? choose the correct answer below. npq √npq √np np

Explanation:

Step1: Recall binomial distribution std - dev formula

The standard - deviation formula for a binomial distribution is based on the parameters \(n\) (number of trials), \(p\) (probability of success on a single trial), and \(q=1 - p\) (probability of failure on a single trial).
The variance of a binomial distribution is \(\sigma^{2}=npq\).

Step2: Find standard - deviation from variance

Since the standard - deviation \(\sigma\) is the square - root of the variance \(\sigma^{2}\), for a binomial distribution \(\sigma=\sqrt{npq}\).

Answer:

\(\sqrt{npq}\) (the second option)