Coffee Sales The following data represent the number of cases of coffee or filters sold by four sales reps in a recent sales competition.
b. What is the probability that a randomly chosen case was Gourmet?

Verified step by step guidance

1. Step 1: Understand the problem. We need to find the probability that a randomly chosen case from all the sales is Gourmet coffee.
2. Step 2: Identify the total number of cases sold. From the table, the total number of cases sold by all salespersons combined is given in the bottom right corner, which is 1009.
3. Step 3: Identify the total number of Gourmet cases sold. From the table, the total number of Gourmet cases sold is given in the bottom of the Gourmet column, which is 264.
4. Step 4: Use the probability formula for an event, which is the number of favorable outcomes divided by the total number of outcomes. Here, the favorable outcomes are the Gourmet cases sold.
5. Step 5: Write the probability expression as \(P(\text{Gourmet}) = \frac{\text{Number of Gourmet cases}}{\text{Total number of cases}} = \frac{264}{1009}\).

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this question, the probability of selecting a Gourmet case is the ratio of Gourmet cases sold to the total cases sold.

Frequency Distribution

A frequency distribution organizes data into categories showing the number of occurrences in each. Here, the table displays the counts of coffee cases sold by type and salesperson, allowing us to see how many Gourmet cases were sold overall and by each rep, which is essential for calculating probabilities.

Marginal Totals

Marginal totals are the sums of rows or columns in a contingency table, representing total counts across categories. The total number of cases sold (1009) is a marginal total, used as the denominator when calculating the probability of selecting a Gourmet case from all sales.