5) Use the following table to answer the probability questions Waiting time Number of customers 0-3 14 4-7 8-11 11 12-15 16-19 20-23 3. 24-27 What is the probability of selecting a customer that waits in line at least 12 minutes? What is the probability of selecting a customer that waits at least 4 minutes?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Probability Analysis Based on Customer Waiting Times**
To understand customer behavior regarding waiting times, consider the following data table which lists the number of customers corresponding to different waiting time intervals.
| **Waiting Time (minutes)** | **Number of Customers** |
|----------------------------|-------------------------|
| 0-3 | 14 |
| 4-7 | 9 |
| 8-11 | 11 |
| 12-15 | 6 |
| 16-19 | 7 |
| 20-23 | 3 |
| 24-27 | 2 |
**Probability Questions:**
1. **What is the probability of selecting a customer that waits in line at least 12 minutes?**
2. **What is the probability of selecting a customer that waits at least 4 minutes?**
**Calculations:**
1. To calculate the probability of a customer waiting at least 12 minutes, sum the number of customers who waited 12 minutes or more, and divide it by the total number of customers.
\[
\text{Total customers waiting at least 12 minutes} = 6 + 7 + 3 + 2 = 18
\]
\[
\text{Total number of customers} = 14 + 9 + 11 + 6 + 7 + 3 + 2 = 52
\]
\[
\text{Probability} = \frac{18}{52} \approx 0.346
\]
2. To calculate the probability of a customer waiting at least 4 minutes, sum the number of customers who waited 4 minutes or more, and divide it by the total number of customers.
\[
\text{Total customers waiting at least 4 minutes} = 9 + 11 + 6 + 7 + 3 + 2 = 38
\]
\[
\text{Total number of customers} = 14 + 9 + 11 + 6 + 7 + 3 + 2 = 52
\]
\[
\text{Probability} = \frac{38}{52} \approx 0.731
\]
These calculations help in understanding the likelihood of different customer waiting periods and are essential for improving service strategies to reduce wait times.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6ad1cd7-e883-4155-acb4-5513247aaa08%2F8ef0110d-a3ee-48ef-a767-a06c24c62234%2F043ttek_processed.jpeg&w=3840&q=75)
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