For binomial distribution `n=10, q=0.4`, then mean is

Options

A. 6
B. `-4`
C. 1
D. 10

Answer

To find the mean of a binomial distribution given \( n = 10 \) and \( q = 0.4 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the parameters of the binomial distribution**:
- We have \( n = 10 \) (the number of trials).
- We have \( q = 0.4 \) (the probability of failure).

2. **Calculate the probability of success \( p \)**:
- The probability of success \( p \) can be calculated using the formula:
\[ p = 1 - q \]
- Substituting the value of \( q \):
\[ p = 1 - 0.4 = 0.6 \]

3. **Use the formula for the mean of a binomial distribution**:
- The mean \( \mu \) of a binomial distribution is given by:
\[ \mu = n \cdot p \]
- Substituting the values of \( n \) and \( p \):
\[ \mu = 10 \cdot 0.6 = 6 \]

4. **Conclusion**:
- Therefore, the mean of the binomial distribution when \( n = 10 \) and \( q = 0.4 \) is:
\[ \mu = 6 \]

### Final Answer:
The mean is \( 6 \).