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To find the mean \(\mu\) for a binomial distribution, you can use the formula:

\[
\mu = n \cdot p
\]

where:
- \(n\) is the number of trials, and
- \(p\) is the probability of success on each trial.

From the problem:
- \(n = 23\)
- \(p = \frac{3}{5} = 0.6\)

Now, let's calculate the mean:

\[
\mu = 23 \cdot 0.6 = 13.8
\]

Therefore, the correct answer is:
**D. \(\mu = 13.8\)**

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:
1. What is the formula for the variance of a binomial distribution?
2. How would you calculate the standard deviation for the same distribution?
3. If \(p\) were \(0.4\) instead of \(0.6\), how would that change the mean?
4. Can a binomial distribution be used for cases where \(p > 1\) or \(n < 0\)? Why or why not?
5. What does the mean represent in the context of a binomial distribution?

**Tip:** The mean of a binomial distribution can be understood as the expected number of successes in \(n\) trials.

Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 23; p = 3/5

Learn how to find the mean of a binomial distribution with n = 23 and p = 3/5. This problem covers probability concepts and the formula for calculating the mean of a binomial distribution. Suitable for students in Grades 9-12.

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