What is the variance of a binomial distance B(8.0.40)

To calculate the variance of a binomial distribution \( B(n, p) \), you can use the formula:

\[
\text{Variance} = n \times p \times (1 - p)
\]

Where:
- \( n \) is the number of trials,
- \( p \) is the probability of success on a single trial.

For the given binomial distribution \( B(8, 0.40) \):

- \( n = 8 \)
- \( p = 0.40 \)

Substituting these values into the formula:

\[
\text{Variance} = 8 \times 0.40 \times (1 - 0.40)
\]

\[
\text{Variance} = 8 \times 0.40 \times 0.60 = 8 \times 0.24 = 1.92
\]

So, the variance of the binomial distribution \( B(8, 0.40) \) is **1.92**.

Would you like more details, or do you have any questions?

Here are five related questions for further exploration:
1. What is the mean of the binomial distribution \( B(8, 0.40) \)?
2. How would the variance change if the probability \( p \) increased to 0.60?
3. What is the standard deviation of this binomial distribution?
4. How does the variance of a binomial distribution change with the number of trials?
5. Can you find the probability of getting exactly 3 successes in this binomial distribution?

**Tip:** The standard deviation of a binomial distribution is simply the square root of the variance.

Learn how to calculate the variance of a binomial distribution B(8, 0.40) with a detailed step-by-step solution. Understand the key concepts of binomial distributions and probability theory. Suitable for students in Grades 11-12.

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