1. What is the Mean of Binomial Distribution?

The mean of a binomial distribution represents the expected number of successes in a given number of trials. It's a fundamental measure of central tendency for binomial experiments.

2. How Does the Calculator Work?

The calculator uses the binomial mean formula:

Where:

• \( n \) — Number of trials (independent experiments)
• \( p \) — Probability of success on each trial
• \( \mu \) — Mean of the binomial distribution

Explanation: The formula shows that the expected number of successes is simply the product of the number of trials and the probability of success in each trial.

3. Importance of Binomial Mean Calculation

Details: Calculating the mean helps predict outcomes in binary scenarios (success/failure), quality control, medical testing, and many other probability applications.

4. Using the Calculator

Tips: Enter number of trials (positive integer) and probability of success (between 0 and 1). All values must be valid (n > 0, 0 ≤ p ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between mean and variance in binomial distribution?
A: While mean (μ = np) gives expected successes, variance (σ² = np(1-p)) measures spread around the mean.

Q2: Can the mean be a non-integer value?
A: Yes, while actual successes must be integers, the expected value (mean) can be fractional.

Q3: What if p > 1 or p < 0?
A: Probability must be between 0 and 1. The calculator will reject invalid values.

Q4: How does increasing n affect the mean?
A: The mean increases linearly with n (more trials → proportionally more expected successes).

Q5: What real-world applications use this calculation?
A: Clinical trials (success rates), manufacturing (defect rates), polling (voting predictions), etc.