A)Compute the expected number of arrivals per minute. B) Compute the standard deviation.   C)What is the probability that there will be fewer than 2 arrivals in a given​ minute?

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A)Compute the expected number of arrivals per minute.

B) Compute the standard deviation.
 
C)What is the probability that there will be fewer than 2 arrivals in a given​ minute?
### Bank Arrivals Per Minute Data Analysis

The following data illustrates the number of customer arrivals per minute at a bank, located in the central business district of a large city. The data was collected over a span of 200 minutes. The frequency of each number of arrivals was recorded and is presented in the table below. This data is useful for analyzing the customer flow and planning resource allocation.

#### Arrivals Data Table

| Arrivals | Frequency |
|----------|-----------|
| 0        | 18        |
| 1        | 39        |
| 2        | 44        |
| 3        | 37        |
| 4        | 26        |
| 5        | 19        |
| 6        | 10        |
| 7        | 5         |
| 8        | 2         |

This histogram shows the distribution of the number of arrivals at the bank per minute:

- **0 arrivals**: There were 0 customers arriving 18 times within the observation period.
- **1 arrival**: 1 customer arrived 39 times within the observation period.
- **2 arrivals**: 2 customers arrived 44 times within the observation period.
- **3 arrivals**: 3 customers arrived 37 times within the observation period.
- **4 arrivals**: 4 customers arrived 26 times within the observation period.
- **5 arrivals**: 5 customers arrived 19 times within the observation period.
- **6 arrivals**: 6 customers arrived 10 times within the observation period.
- **7 arrivals**: 7 customers arrived 5 times within the observation period.
- **8 arrivals**: 8 customers arrived 2 times within the observation period.

### Analysis
The data shows that the number of arrivals per minute varies significantly. Noteworthy points include:

- The most frequent number of arrivals per minute is 2, happening 44 times.
- Occasions with no arrivals were recorded 18 times, making it the second least frequent after 8 arrivals.
- There is a decreasing trend in frequency as the number of arrivals increases beyond 2 arrivals per minute.

Use this data for further statistical analysis to understand customer behavior and optimize staffing and operations accordingly.
Transcribed Image Text:### Bank Arrivals Per Minute Data Analysis The following data illustrates the number of customer arrivals per minute at a bank, located in the central business district of a large city. The data was collected over a span of 200 minutes. The frequency of each number of arrivals was recorded and is presented in the table below. This data is useful for analyzing the customer flow and planning resource allocation. #### Arrivals Data Table | Arrivals | Frequency | |----------|-----------| | 0 | 18 | | 1 | 39 | | 2 | 44 | | 3 | 37 | | 4 | 26 | | 5 | 19 | | 6 | 10 | | 7 | 5 | | 8 | 2 | This histogram shows the distribution of the number of arrivals at the bank per minute: - **0 arrivals**: There were 0 customers arriving 18 times within the observation period. - **1 arrival**: 1 customer arrived 39 times within the observation period. - **2 arrivals**: 2 customers arrived 44 times within the observation period. - **3 arrivals**: 3 customers arrived 37 times within the observation period. - **4 arrivals**: 4 customers arrived 26 times within the observation period. - **5 arrivals**: 5 customers arrived 19 times within the observation period. - **6 arrivals**: 6 customers arrived 10 times within the observation period. - **7 arrivals**: 7 customers arrived 5 times within the observation period. - **8 arrivals**: 8 customers arrived 2 times within the observation period. ### Analysis The data shows that the number of arrivals per minute varies significantly. Noteworthy points include: - The most frequent number of arrivals per minute is 2, happening 44 times. - Occasions with no arrivals were recorded 18 times, making it the second least frequent after 8 arrivals. - There is a decreasing trend in frequency as the number of arrivals increases beyond 2 arrivals per minute. Use this data for further statistical analysis to understand customer behavior and optimize staffing and operations accordingly.
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