A sample of 120 local residents reveals that 8 have a post office box for receiving mail. What is the relative frequency that a local resident does not have a post office box for receiving mail?

A. 14over15

B. 4over5

C. 1over15

D. 46over50


To determine the relative frequency that a local resident does not have a post office box for receiving mail, we need to calculate the proportion of residents who do not have a post office box.

First, find the number of residents who do not have a post office box:
- Total number of residents: \( 120 \)
- Number of residents with a post office box: \( 8 \)

So, the number of residents without a post office box is:
\[ 120 - 8 = 112 \]

Next, calculate the relative frequency:
\[ \text{Relative frequency} = \frac{\text{Number of residents without a post office box}}{\text{Total number of residents}} = \frac{112}{120} \]

Now, simplify the fraction \(\frac{112}{120}\):
- Find the greatest common divisor (GCD) of 112 and 120. The GCD is 8.
- Divide both the numerator and the denominator by their GCD:

\[ \frac{112 \div 8}{120 \div 8} = \frac{14}{15} \]

Therefore, the relative frequency that a local resident does not have a post office box for receiving mail is:
\[ \boxed{\frac{14}{15}} \]

The correct answer is:

A. \(\frac{14}{15}\)

Would you like further details or have any questions? Here are some related questions to explore this topic:

1. How do you find the greatest common divisor (GCD) of two numbers?
2. What is the difference between relative frequency and absolute frequency?
3. How can you convert a fraction to a decimal?
4. How can you convert a fraction to a percentage?
5. What are some real-world applications of relative frequency?
6. How do you simplify fractions?
7. How can you verify the accuracy of your fraction simplification?
8. What is the formula for relative frequency in general terms?

**Tip:** To simplify fractions effectively, always look for the greatest common divisor (GCD) and divide both the numerator and denominator by it.

Learn how to calculate the relative frequency that local residents do not have a post office box for receiving mail. This problem involves statistics and probability, focusing on fraction simplification to determine the correct answer among given choices. Suitable for students in Grades 7-9.

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