Nick surveyed a random sample of the freshman class of his high school to determine whether the Fall Festival should be held in October or November. Of the 90 students surveyed, 25.6% preferred October. Based on this information, about how many students in the entire 225-person class would be expected to prefer having the Fall Festival in October?

Options

A. 50
B. 60
C. 75
D. 80

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Problem
We need to determine how many students in a class of 225 would prefer having the Fall Festival in October based on the survey results from a sample of 90 students.

**Hint:** Identify the total number of students and the percentage from the survey that indicates preference.

### Step 2: Calculate the Percentage of Students Preferring October
From the survey, we know that 25.6% of the 90 students preferred October.

**Hint:** Remember that percentage can be converted to a decimal for calculations (25.6% = 0.256).

### Step 3: Apply the Percentage to the Total Class Size
To find out how many students in the entire class of 225 would prefer October, we can multiply the total number of students by the percentage of students who prefer October.

\[ \text{Number of students preferring October} = 225 \times 0.256 \]

### Step 4: Perform the Calculation
Now, we will perform the multiplication:

\[ 225 \times 0.256 = 57.6 \]

Since we cannot have a fraction of a student, we round this number to the nearest whole number.

**Hint:** When rounding, consider whether to round up or down based on the decimal value.

### Step 5: Round the Result
Rounding 57.6 gives us approximately 58 students.

### Step 6: Conclusion
Based on the survey, we can expect that about 58 students in the entire 225-person class would prefer having the Fall Festival in October.

**Final Answer:** Approximately 58 students would prefer having the Fall Festival in October.

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