Question

practice problems: answer the questions below given each situation and the data collected
there are 150 residents at the local senior citizen assisted living home. sixty names were drawn at random and those residents were asked to list their favorite breakfast item available at the cafeteria. the results of the 60-person sample are shown below. assuming the sample is valid and represents the population of the assisted living home, fill in the table with the inferences about the population: (1) population: the number of total residents that would most likely have chosen that breakfast item had each resident been polled, and (2) percentage %: the percentage of the population this number represents.

breakfast | sample | population | %
eggs + bacon | 15 | 37.5 | 25%
oatmeal | 20 | 50 | 30%
protein shake | 9 | 7.5 | 15%
pancakes/waffles | 12 | |
toast + yogurt | 4 | |

hint:
population: set up a ratio
survey part : survey total = x : total population
percent:
survey part / survey total * 100 = %

Explanation:

Step1: Find sample-population ratio

$\text{Ratio} = \frac{150}{60} = 2.5$

Step2: Calculate Population for Protein Shake

$9 \times 2.5 = 22.5$

Step3: Calculate % for Protein Shake

$\frac{9}{60} \times 100 = 15\%$

Step4: Calculate Population for Pancakes/Waffles

$12 \times 2.5 = 30$

Step5: Calculate % for Pancakes/Waffles

$\frac{12}{60} \times 100 = 20\%$

Step6: Calculate Population for Toast + Yogurt

$4 \times 2.5 = 10$

Step7: Calculate % for Toast + Yogurt

$\frac{4}{60} \times 100 \approx 6.67\%$

Answer:

Breakfast Item	Sample	Population	%
Oatmeal	20	50	33.33%
Protein Shake	9	22.5	15%
Pancakes/Waffles	12	30	20%
Toast + Yogurt	4	10	6.67%

Note: Corrected Eggs + Bacon percentage to $\frac{15}{60} \times 100 = 25\%$ and Oatmeal percentage to $\frac{20}{60} \times 100 \approx 33.33\%$ for accuracy, as the initial table values had calculation errors.