Let the mean success rate of a Poisson process be 10 successes per hour.

Find the expected number of successes in a 22 minutes period

In a Poisson process, the mean number of successes (or events) in a given time period is proportional to the length of that period.

### Given:
- Mean success rate = 10 successes per hour.
- We need to find the expected number of successes in a 22-minute period.

Since 22 minutes is a fraction of an hour, we first convert it to hours:
\[
22 \, \text{minutes} = \frac{22}{60} \, \text{hours} \approx 0.3667 \, \text{hours}
\]

Now, multiply the mean success rate by the time period (in hours):
\[
\text{Expected number of successes} = 10 \times 0.3667 \approx 3.667
\]

Thus, the expected number of successes in a 22-minute period is approximately **3.67**.

Would you like further details on Poisson processes or any additional clarifications?

Here are some related questions for further exploration:
1. What is the probability of having exactly 3 successes in a 22-minute period?
2. How do you calculate the variance in the number of successes in a Poisson process?
3. What is the probability of having no successes in a 22-minute period?
4. How does the Poisson distribution change as the rate of success increases?
5. Can the Poisson process be applied to non-time-based events, such as spatial occurrences?

**Tip:** The Poisson distribution is used to model rare events happening within a fixed period of time or space.

Let the mean success rate of a Poisson process be 10 successes per hour. Find the expected number of successes in a 22 minutes period.

Find the expected number of successes in a 22-minute period for a Poisson process with a mean success rate of 10 per hour. This problem involves key concepts such as expected value and the Poisson distribution, suitable for students in Grades 11-12 or college.

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