FPGEE for National Association of Boards of Pharmacy (NABP) Practice Exam 2025 - Free NABP Practice Questions and Study Guide

In a binomial distribution, the mean is calculated using the formula \( \mu = n \cdot p \), where \( n \) represents the number of trials, and \( p \) is the probability of success on an individual trial. This formula indicates that the mean is directly proportional to both the number of trials conducted and the probability of success for each trial.

For instance, if you have a binomial experiment with more trials, or if the probability of success in each trial is higher, the mean will increase accordingly. This concept helps in understanding the expected number of successes in a fixed number of trials, making it a crucial aspect of probability and statistics in various applied fields, including pharmacy.

In contrast, other options do not apply to the mean of a binomial distribution. The sum of \( n \) and \( p \), dividing \( n \) by \( p \), or subtracting \( p \) from \( n \) do not yield a meaningful measure of successes in this context. Therefore, the formula \( n \cdot p \) is the correct representation of the mean in a binomial distribution.