Question

Use the following for questions 9–10. Angela is a supervisor at a department store. She developed this chart to check the dollar amount of sales made by various salespersons. $$ \begin{array}{|c|c|} \hline \text { Sales } & \text { \\# Salespersons } \\ \hline \$ 0-\$ 50 & 1 \\ \hline \$ 51-\$ 100 & 3 \\ \hline \$ 101-\$ 150 & 7 \\ \hline \$ 151-\$ 200 & 6 \\ \hline \$ 201-\$ 250 & 4 \\ \hline \end{array} $$ If a salesperson is picked at random, what is the probability that a person who sold between \(\$ 201\) and \(\$ 250\) worth of merchandise will be chosen? A. \(\frac{4}{21}\) B. \(\frac{6}{21}\) C. \(\frac{10}{21}\) D. \(\frac{17}{21}\)

Short answer

The probability is \( \frac{4}{21} \).

Step-by-step solution

Identify the total number of salespersons

Calculate the total number of salespersons by adding up all the salespersons in each category. Total number of salespersons = 1 + 3 + 7 + 6 + 4

Find the total number of salespersons who sold between \(201 and \)250

From the given chart, the number of salespersons who sold between \(201 and \)250 is 4.

Calculate the probability

Use the probability formula: Probability = \( \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Here, the favorable outcomes are the salespersons who sold between \(201 and \)250, and the total number of outcomes is the total number of salespersons. \( \text{Probability} = \frac{4}{21} \).

Key concepts

Probability

Probability is a way to measure how likely it is for an event to happen. To find the probability, you use the formula:

• Probability = \( \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \)

In this exercise, we need to find the probability that a salesperson randomly picked sold between \( \$ 201 \) and \( \$ 250 \) worth of merchandise. First, count all the salespersons, which totals 21. Then, count those who sold between \( \$ 201 \) and \( \$ 250 \), which is 4. Plug those values into the formula:

• Probability = \( \frac{4}{21} \)

So, there is a 4 in 21 chance of picking a salesperson who sold that amount.

Mathematical Reasoning

Mathematical reasoning helps us solve problems step-by-step logically. In this problem, we follow these steps:

• First, gather all data (from the chart).
• Next, sum all numbers to get the total number of salespersons.
• Identify the number of favorable outcomes, which is the salespersons who sold within the required range.

This logical approach ensures that we account for all relevant information and avoid mistakes. By breaking a problem down into smaller, manageable parts, we can see the path to the solution more clearly.

Data Interpretation

Data interpretation involves understanding and using data effectively. For this exercise, interpret the chart that shows sales distribution among salespersons.

• Look at the chart to see how many salespersons fall into each sales category (e.g., \$ 0 - \$ 50, \$ 51 - \$ 100, etc.).
• Summing these numbers gives the total number of salespersons (21).
• Observe that 4 salespersons made sales between \( \$ 201 \) and \( \$ 250 \).

By interpreting this data correctly, you calculate the exact probability of selecting a salesperson from the desired sales range. It’s crucial to read the data accurately to make correct calculations.

Basic Arithmetic

Basic arithmetic involves simple calculations like addition and division, which you use in probability problems. Here's a breakdown of the necessary arithmetic steps:

• Add the number of salespersons in each category: 1 + 3 + 7 + 6 + 4.
• The sum (21) is the total number of salespersons.
• To find the probability, divide the number of favorable outcomes by the total number of outcomes: \( \frac{4}{21} \).

These simple arithmetic operations are fundamental to solving the problem and understanding basic probability concepts. Mastering these ensures you can tackle more complex problems with ease.