Question: In a certain population of birds, about 40 percent of the birds have a wingspan greater than 10 inches.
Biologists studying the birds will create a simulation with random numbers to estimate the probability of
finding one bird in a sample of six birds with a wingspan greater than 10 inches.
9 Mark for Review
Which of the following assignments of the digits 0 to 9 will model the population?
A Let the even digits represent birds with a wingspan greater than 10 inches and
the odd digits represent birds with a wingspan less than or equal to 10 inches.
B Let the digits from 0 to 2 represent birds with a wingspan greater than 10 inches
and the remaining digits represent birds with a wingspan less than or equal to
10 inches.
C Let the digits from 0 to 3 represent birds with a wingspan greater than 10 inches
and the remaining digits represent birds with a wingspan less than or equal to
10 inches.
D Let the digits from 0 to 4 represent birds with a wingspan greater than 10 inches
and the remaining digits represent birds with a wingspan less than or equal to
10 inches.
1. **State the problem:** We want to model a population where about $40\%$ of birds have a wingspan greater than 10 inches using digits 0 to 9.
2. **Understand the modeling:** The digits 0 to 9 represent birds. We assign some digits to represent birds with wingspan > 10 inches and the rest to wingspan \leq 10 inches.
3. **Calculate the proportion for each option:**
- Option A: Even digits are greater than 10 inches. Even digits are $0,2,4,6,8$ which is 5 digits.
Proportion = $\frac{5}{10} = 0.5 = 50\%$
- Option B: Digits 0 to 2 represent > 10 inches. These are $0,1,2$ which is 3 digits.
Proportion = $\frac{3}{10} = 0.3 = 30\%$
- Option C: Digits 0 to 3 represent > 10 inches. These are $0,1,2,3$ which is 4 digits.
Proportion = $\frac{4}{10} = 0.4 = 40\%$
- Option D: Digits 0 to 4 represent > 10 inches. These are $0,1,2,3,4$ which is 5 digits.
Proportion = $\frac{5}{10} = 0.5 = 50\%$
4. **Compare to the target 40\%:**
Only Option C matches the $40\%$ proportion exactly.
**Final answer:** Option C models the population correctly.