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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A)Compute the expected number of arrivals per 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90030b31-8456-491f-aeee-bd0f02cf8e6c%2Fab68df55-26b6-4660-9b7b-7f64680c372d%2Fp24u7ao_processed.png&w=3840&q=75)
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