Question

health the florida department of health surveyed individuals aged 18 to 44 regarding their mental health. of these, 84.4% reported having good mental health in the last 30 days. the survey had a margin of error of 2.7%.
estimate the range of the actual percentages of people aged 18 to 44 in florida who would report having good mental health in the last 30 days.
____% to ____%
of the estimated 6.46 million floridians aged 18 to 44, how many would you expect to report having good mental health in the last 30 days? use your estimated range to solve. round to the nearest hundredth.
between ____ million and ____ million

Explanation:

Part 1: Estimate the range of percentages

Step1: Find lower bound

Subtract margin of error from reported percentage.
$84.4\% - 2.1\% = 82.3\%$

Step2: Find upper bound

Add margin of error to reported percentage.
$84.4\% + 2.1\% = 86.5\%$

Step1: Calculate lower number

Multiply lower percentage (as decimal) by total population.
$6.46 \times 0.823 = 6.46 \times 0.823 \approx 5.31658 \approx 5.32$ (million)

Step2: Calculate upper number

Multiply upper percentage (as decimal) by total population.
$6.46 \times 0.865 = 6.46 \times 0.865 \approx 5.5879 \approx 5.59$ (million)

Answer:

82.3% to 86.5%

Part 2: Estimate the number of people