The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200​ minutes, with the results shown in the table below. Complete​ (a) through​ (c) to the right. Arrivals (x)	Frequency (f)
0	8
1	20
2	48
3	43
4	33
5	25
6	13
7	7
8	3 Compute the expected number of arrivals per minute. Type an integer or decimal rounded to three decimal places as​ needed.)

To find the expected number of arrivals per minute, we need to calculate the weighted average of arrivals. This can be done using the formula for the expected value \( E(X) \):

\[
E(X) = \sum (x \cdot P(x))
\]

Where:
- \( x \) is the number of arrivals,
- \( P(x) \) is the probability of each arrival value, which is given by \( P(x) = \frac{f}{N} \), where \( f \) is the frequency and \( N \) is the total number of observations.

Given dataTo find the expected number of arrivals per minute, we need to calculate the weighted average of arrivals. This can be done using the formula for the expected value \( E(X) \):

\[
E(X) = \sum (x \cdot P(x))
\]

Where:
- \( x \) is the number of arrivals,
- \( P(x) \) is the probability of each arrival value, which is given by \( P(x) = \frac{f}{N} \), where \( f \) is the frequency and \( N \) is the total number of observations.

Given 
- Frequencies \( f \): 8, 20, 48, 43, 33, 25, 13, 7, 3
- Total observations \( N = 8 + 20 + 48 + 43 + 33 + 25 + 13 + 7 + 3 = 200 \)

Now, let's compute the expected number of arrivals step by step:

1. Multiply each number of arrivals \( x \) by its corresponding frequency \( f \) to get \( x \cdot f \).
2. Sum up all the products from step 1.
3. Divide the sum by the total number of observations \( N \).

Let's calculate this.The expected number of arrivals per minute is approximately \( 3.265 \).

Would you like further details or have any questions?

Here are 5 related questions that build on this information:
1. What is the variance of the number of arrivals per minute?
2. How do you interpret the expected number of arrivals in a real-world context?
3. What would the expected number of arrivals be if the observation period was different?
4. How does the shape of the distribution affect the expected number of arrivals?
5. What if the bank changes its operation hours? How would this affect the expected number of arrivals?

**Tip:** When interpreting the expected value, remember it represents the long-run average if the experiment is repeated many times. It may not always be an observable value in a single experiment.

The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200​ minutes, with the results shown in the table below. Complete​ (a) through​ (c) to the right. Arrivals (x) Frequency (f) 0 8, 1 20, 2 48, 3 43, 4 33, 5 25, 6 13, 7 7, 8 3 Compute the expected number of arrivals per minute. Type an integer or decimal rounded to three decimal places as​ needed.

Find out how to compute the expected number of arrivals per minute in a bank located in the central business district over a 200-minute period. This problem covers key statistical concepts like expected value and probability distribution, making it suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation