Which of the following formulas is the easiest way to calculate the mean of a binomial distribution?

• A. $n+p$
• B. $n\times p$
• C. $\frac{n}{p}$
• D. $\sqrt{n\times p\times (1-p)}$

Answer: (B)

Verified step by step guidance

1. Recall that a binomial distribution models the number of successes in \( n \) independent trials, each with success probability \( p \).
2. The mean (or expected value) of a binomial distribution is given by the formula \( \mu = n \times p \).
3. This formula represents the average number of successes you would expect over \( n \) trials.
4. Other formulas given, such as \( n + p \), \( \frac{n}{p} \), or \( \sqrt{n \times p \times (1 - p)} \), correspond to different statistics (e.g., variance or standard deviation) or are incorrect for the mean.
5. Therefore, the easiest and correct way to calculate the mean of a binomial distribution is to multiply the number of trials \( n \) by the probability of success \( p \), i.e., \( \mu = n \times p \).