A college cafeteria is looking for a new dessert to offer its 5,000 students. The table shows the preference of 225 students.
| Ice Cream | Candy | Cake | Pie | Cookies |
|---|---|---|---|---|
| 81 | 9 | 72 | 36 | 27 |
Which statement is the best prediction about the scoops of ice cream the college will need?
A. The college will have about 1,800 students who prefer ice cream.
B. The college will have about 800 students who prefer ice cream.
C. The college will have about 600 students who prefer ice cream.
D. The college will have about 144 students who prefer ice cream.
Answer (2)
After calculating the proportion of students who prefer ice cream and applying that to the total student body of 5,000, we estimate that around 1,800 students will have a preference for ice cream. Thus, the best prediction is option A. The college will have about 1,800 students who prefer ice cream.
;
Calculate the proportion of students who prefer ice cream: 225 81 = 25 9 .
Multiply the proportion by the total number of students: 5000 × 25 9 .
Simplify the expression: 25 5000 × 9 = 200 × 9 .
The estimated number of students who prefer ice cream is: 1800 .
Explanation
Analyze the problem and data We are given the dessert preferences of 225 students and need to predict the preferences of 5,000 students. The key is to find the proportion of students who prefer ice cream in the sample and apply that proportion to the entire student population.
Calculate the proportion of students who prefer ice cream First, we calculate the proportion of students in the survey who prefer ice cream. From the table, we see that 81 out of 225 students prefer ice cream. So, the proportion is: p = 225 81
Simplify the fraction Now, we simplify the fraction: p = 225 81 = 9 × 25 9 × 9 = 25 9
Estimate the number of students who prefer ice cream Next, we multiply this proportion by the total number of students in the college (5,000) to estimate the number of students who prefer ice cream: N = 5000 × 25 9
Calculate the final estimation Now, we perform the calculation: N = 5000 × 25 9 = 25 5000 × 9 = 200 × 9 = 1800
State the final answer Therefore, we estimate that 1,800 students in the college prefer ice cream.
Examples
Imagine you're planning a school event and need to decide how much of each type of food to order. By surveying a smaller group of students, you can estimate the preferences of the entire student body. For example, if you survey 200 students and find that 50 prefer pizza, you can estimate that about 25% of the entire school population also prefers pizza. If the school has 1000 students, you would then order enough pizza for approximately 250 students. This helps ensure you have enough of what people like and avoid wasting resources on unpopular items.
