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The image shows a table of the number of arrivals per minute at a bank and the corresponding frequency over a period of 200 minutes. The goal is to compute the expected number of arrivals per minute, denoted as \( \mu \).

The table is structured as:

| Arrivals (X) | Frequency (f) |
|--------------|---------------|
| 0            | 15            |
| 1            | 33            |
| 2            | 49            |
| 3            | 42            |
| 4            | 28            |
| 5            | 18            |
| 6            | 9             |
| 7            | 4             |
| 8            | 2             |

The expected number of arrivals \( \mu \) is calculated using the formula for the expected value (mean) of a discrete random variable:
\[
\mu = \frac{\sum (X \cdot f)}{\sum f}
\]
Where:
- \( X \) is the number of arrivals,
- \( f \) is the frequency.

Let me compute that for you.The expected number of arrivals per minute, \( \mu \), is approximately \( 2.785 \) (rounded to three decimal places).

Would you like more details or have any other questions? Here are some related questions to explore:

1. How would you calculate the variance of the number of arrivals?
2. What is the probability of having exactly 3 arrivals in a minute?
3. How would the expected value change if the frequency of arrivals of 6 were doubled?
4. Can you explain the significance of the expected number of arrivals?
5. How would you compute the median number of arrivals based on this data?

**Tip**: Always double-check the total frequency to ensure the data you're working with matches the context of the problem.

Compute the expected number of arrivals per minute at a bank based on the provided frequency data.

Learn how to calculate the expected number of arrivals per minute at a bank using provided frequency data over 200 minutes. This problem involves calculating the mean using the expected value formula, making it ideal for students studying introductory statistics.

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