Question

practice problems: answer the questions below given each situation and the data collected.
1 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 | 33.33%
protein shake | 9 | 22.5 | 15%
pancakes/waffles | 12 | 30 | 20%
toast + yogurt | 4 | 10 | 6.67

hint:
population: set up a key!
$\frac{survey part}{survey total}$ = $\frac{x}{total population}$
percent:
$\frac{survey part}{survey total}$ times 100 = %

the local high school has 250 seniors in this years graduating class. a random name generator produced the names of 50 seniors from the full-class roster. these 50 students were surveyed and asked if they participated in any after-school activities. the results are shown in the table below. answer the questions based on the data given.
2 approximately what
3 about how many total

Explanation:

Step1: Verify Population for Eggs + Bacon

Set up proportion: $\frac{15}{60} = \frac{x}{150}$
Solve for $x$: $x = \frac{15 \times 150}{60} = 37.5$

Step2: Verify % for Eggs + Bacon

Calculate percentage: $\frac{15}{60} \times 100 = 25\%$

Step3: Verify Population for Oatmeal

Set up proportion: $\frac{20}{60} = \frac{x}{150}$
Solve for $x$: $x = \frac{20 \times 150}{60} = 50$

Step4: Verify % for Oatmeal

Calculate percentage: $\frac{20}{60} \times 100 \approx 33.33\%$

Step5: Verify Population for Protein Shake

Set up proportion: $\frac{9}{60} = \frac{x}{150}$
Solve for $x$: $x = \frac{9 \times 150}{60} = 22.5$

Step6: Verify % for Protein Shake

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

Step7: Verify Population for Pancakes/Waffles

Set up proportion: $\frac{12}{60} = \frac{x}{150}$
Solve for $x$: $x = \frac{12 \times 150}{60} = 30$

Step8: Verify % for Pancakes/Waffles

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

Step9: Verify Population for Toast + Yogurt

Set up proportion: $\frac{4}{60} = \frac{x}{150}$
Solve for $x$: $x = \frac{4 \times 150}{60} = 10$

Step10: Verify % for Toast + Yogurt

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

Answer:

The completed table values are all verified as correct:

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