Question

donors according to a survey conducted by the u.s. department of health and human services, about 50% of u.s. adults age 18 and older as organ donors. the survey had a margin of error of ±1.2%. estimate the range of the actual percentages of u.s. adults who are registered organ donors. □% to □% in 2019, there were an estimated 255,200,373 adults age 18 and older. use your estimated range to estimate the total number of u.s. adults who registered organ donors to the nearest hundred thousand. between □ million and □ million u.s. adults

Explanation:

Part 1: Estimate the percentage range

Step1: Find the lower bound

To find the lower bound of the percentage, we subtract the margin of error from the given percentage. The given percentage is \( 50\% \) and the margin of error is \( 1.2\% \). So, the lower bound is \( 50 - 1.2 = 48.8\% \).

Step2: Find the upper bound

To find the upper bound of the percentage, we add the margin of error to the given percentage. So, the upper bound is \( 50 + 1.2 = 51.2\% \).

Step1: Calculate the lower bound of the number of donors

First, convert the lower percentage (\( 48.8\% \)) to a decimal by dividing by 100, so \( 48.8\% = 0.488 \). Then multiply this by the total number of adults (\( 255200373 \)): \( 255200373\times0.488 \approx 255200373\times0.488 \). Let's calculate this: \( 255200373\times0.488 \approx 124537782.024 \). Now, round to the nearest hundred thousand. The hundred thousand place is the 5th digit from the right. \( 124537782.024 \approx 124500000 \) (since the ten thousand digit is 3, which is less than 5, we round down). Convert to million: \( \frac{124500000}{1000000} = 124.5 \) million.

Step2: Calculate the upper bound of the number of donors

Convert the upper percentage (\( 51.2\% \)) to a decimal: \( 51.2\% = 0.512 \). Multiply by the total number of adults: \( 255200373\times0.512 \approx 255200373\times0.512 \). Calculating this: \( 255200373\times0.512 \approx 130662590.976 \). Round to the nearest hundred thousand. The ten thousand digit is 6, which is greater than 5, so we round up. \( 130662590.976 \approx 130700000 \). Convert to million: \( \frac{130700000}{1000000} = 130.7 \) million.

Answer:

\( 48.8\% \) to \( 51.2\% \)

Part 2: Estimate the number of organ donors