Question

Angela is a supervisor at a department store. She developed this chart to check the dollar amount of sales made by various salespersons. $$ \begin{array}{|c|c|} \hline \text { Sales } & \text { \\# Salespersons } \\ \hline \$ 0-\$ 50 & 1 \\ \hline \$ 51-\$ 100 & 3 \\ \hline \$ 101-\$ 150 & 7 \\ \hline \$ 151-\$ 200 & 6 \\ \hline \$ 201-\$ 250 & 4 \\ \hline \end{array} $$ What is the probability that a salesperson picked at random will have sold more than \(\$ 150\) worth of merchandise? A. \(\frac{4}{21}\) B. \(\frac{6}{21}\) C. \(\frac{10}{21}\) D. \(\frac{17}{21}\)

Short answer

Option C: \( \frac{10}{21} \).

Step-by-step solution

Determine the total number of salespersons

Add the number of salespersons in each sales range: 1 + 3 + 7 + 6 + 4. This gives us the total number of salespersons.

Calculate total number of salespersons

Perform the addition: 1 + 3 + 7 + 6 + 4 = 21. Hence, there are 21 salespersons in total.

Identify the salespersons who sold more than \( \$ 150 \)

Look at the chart: the salespersons who sold more than \( \$ 150 \) fall into the \( \$ 151-\$ 200 \) and \( \$ 201-\$ 250 \) ranges. There are 6 plus 4 salespersons in these ranges.

Compute the number of salespersons who sold more than \( \$ 150 \)

Perform the addition: 6 + 4 = 10. Therefore, 10 salespersons sold more than \( \$ 150 \).

Calculate probability of randomly picking a salesperson who sold more than \( \$ 150 \) worth of merchandise

Use the probability formula: Divide the number of favorable outcomes by the total number of outcomes: \( \frac{10}{21} \).

Match the fraction with the given options

Compare \( \frac{10}{21} \) with the answers provided: Option C.

Key concepts

GED Math

The GED (General Educational Development) math section covers a wide range of topics, including basic algebra, geometry, and probability. In the given exercise, understanding the probability concept is crucial because it forms part of what you may encounter in a GED math test. To excel in this section, practice breaking down problems into smaller steps, as we've done here. Each step builds on the previous one, helping to ensure you understand the overall problem. Review the steps methodically: determine totals, identify relevant data, perform calculations, and finally, interpret the results. Regular practice with problems like these will improve both your comprehension and speed.

Sales Data Analysis

Sales data analysis is essential for supervisors and business analysts. It involves examining and interpreting data to make informed decisions. In the given problem, Angela developed a chart to monitor sales performance. Knowing how to read and analyze such charts is vital:
- Identify ranges and corresponding values.
- Sum up relevant figures to get meaningful insights.
- Calculate probabilities for predictions.
By systematically approaching the problem, you can deduce essential patterns and probabilities, enabling better decision-making. For instance, Angela can determine the likelihood of a salesperson achieving sales above a specific threshold, helping in setting realistic sales goals and identifying top performers.

Probability

Probability is a measure of how likely an event is to occur. It's calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In our exercise:
1. We determined the total number of salespersons (21).
2. We identified those who sold more than $150 (10).
3. Then, we divided 10 by 21 to find the probability: \( \frac{10}{21} \).
This concept can be applied in various real-world scenarios to predict outcomes and make decisions based on likelihood. Regular practice with probability problems will enhance your ability to estimate and interpret data effectively.