Each year a company selects a number of employees for a management training program. On average, 40 percent of those sent complete the program. Out of the 29 people sent, what is the probability that exactly 6 complete the program?
 0.0153


 0.2153


 0.0593


 0.1233


 0.0233


 None of the above

This problem involves finding the probability of exactly 6 people completing the management training program, given that the completion rate is 40%. This scenario follows a **binomial distribution** since:

- Each employee either completes or does not complete the program (two outcomes).
- The probability of completing the program is constant (40%).
- There are a fixed number of trials (29 employees).

The binomial probability formula is:

\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]

Where:
- \(n = 29\) (number of employees sent),
- \(k = 6\) (number of employees who complete the program),
- \(p = 0.4\) (probability of completing the program).

Let’s calculate this probability using the binomial distribution formula.The probability that exactly 6 out of 29 employees complete the program is approximately **0.0154**, which rounds to **0.0153**.

Thus, the correct answer is:

**0.0153**.

Would you like further details on how this was calculated or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the probability that at least 10 employees complete the program?
2. How does the probability change if the completion rate increases to 50%?
3. What is the expected number of employees to complete the program?
4. How do we calculate the standard deviation of this binomial distribution?
5. What if we wanted the probability that fewer than 6 employees complete the program?

**Tip:** The binomial distribution is useful when dealing with discrete events that have two possible outcomes across several trials.

Each year a company selects a number of employees for a management training program. On average, 40 percent of those sent complete the program. Out of the 29 people sent, what is the probability that exactly 6 complete the program?

0.0153

0.2153

0.0593

0.1233

0.0233

None of the above

Find the probability that exactly 6 out of 29 employees complete a management training program, given a 40% completion rate. This problem demonstrates the use of the binomial distribution formula to calculate probabilities in real-world scenarios. Suitable for Grades 10-12 and college introductory statistics.

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