Question

In a Binomial distribution with \(n=10\) and \(p=0.4\), find the variance.

• A. \(2.0\)
• B. \(2.4\)
• C. \(4.0\)
• D. \(3.2\)

Hint:

For a binomial distribution: Mean \(= np\) Variance \(= npq\) Standard deviation \(=\sqrt{npq}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the calculation of variance for a Binomial distribution given the number of trials and the probability of success.
Step 2: Key Formula or Approach:
For a Binomial distribution \(B(n, p)\):
- Mean = \(np\)
- Variance (\(\sigma^2\)) = \(npq\)
where \(q = 1 - p\) is the probability of failure.
Step 3: Detailed Explanation:
Given parameters:
\(n = 10\)
\(p = 0.4\)
First, calculate the probability of failure \(q\):
\[ q = 1 - p = 1 - 0.4 = 0.6 \]
Now, calculate the variance:
\[ \text{Variance} = n \times p \times q \]
\[ \text{Variance} = 10 \times 0.4 \times 0.6 \]
\[ \text{Variance} = 4 \times 0.6 \]
\[ \text{Variance} = 2.4 \]
Step 4: Final Answer:
The variance of the given Binomial distribution is 2.4.