At a recent baseball game with 7,525 people in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
| Ketchup | Mustard | Chili |
|---|---|---|
| 63 | 27 | 60 |
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
Answer (2)
Calculate the proportion of people who prefer mustard: 150 27 .
Multiply the proportion by the total attendance: 150 27 \tims 7525 = 1354.5 .
Round the result to the nearest whole number: 1354.5 ≈ 1355 .
The estimated number of people who prefer mustard is: 1 , 355 .
Explanation
Understand the problem We are given the attendance at a baseball game (7,525 people) and the results of a survey of 150 people about their hot dog topping preferences. We want to estimate how many people in the total attendance would prefer mustard, based on the survey data.
Calculate the proportion First, we need to find the proportion of people in the sample who prefer mustard. From the table, we see that 27 out of 150 people prefer mustard. So, the proportion is: 150 27
Estimate the number of people Now, we will multiply this proportion by the total attendance to estimate the number of people who prefer mustard: 150 27 × 7525
Round to the nearest whole number The result of this calculation is 1354.5. Since we can't have half a person, we round this to the nearest whole number, which is 1355.
State the final answer Therefore, based on the sample data, we estimate that 1355 people in attendance would prefer mustard on their hot dog.
Examples
Imagine you are planning catering for a large event, like a baseball game. Knowing the preferences of a sample of attendees can help you estimate how much of each topping (ketchup, mustard, chili) to provide. By surveying a smaller group and scaling up the results, you can make informed decisions about your inventory, ensuring you have enough of what people want without overstocking items that are less popular. For example, if you know that approximately 150 27 of people like mustard, you can use this fraction to estimate the demand from a larger crowd. In our case, we found that about 1355 people would prefer mustard.
Based on the survey data indicating that 27 out of 150 people prefer mustard on a hot dog, we estimate that approximately 1,355 attendees at the baseball game would prefer mustard. This estimate is calculated by multiplying the proportion of mustard preference by the total attendance of 7,525. Thus, we conclude that around 1,355 people would choose mustard as their hot dog topping.
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