Question

students at a certain school have to take an arts or technology class. a random sample of 60 students from the school are surveyed. each student is asked which class they take. based on the survey results, which of these statements about students at the school are true? select all the correct answers. a there are many excellent dancers at the school. b about 25% of the students take painting. c for every 30 students, about 11 take photography. d next year, 7 out of every 60 students will take music. e in a group of 120 students, about 16 likely take engineering. class number of students dance 19 engineering 8 music 7 painting 15 photography 11

Explanation:

Step1: Calculate total surveyed students

$19 + 8 + 7 + 15 + 11 = 60$

Step2: Evaluate Option A

No data on "excellent dancers" provided. Eliminate A.

Step3: Evaluate Option B

Painting proportion: $\frac{15}{60} = 25\%$, but the option says "painting" is a class, yet the survey only represents current data as a sample, and the statement frames it as a general claim without tying to the sample properly. Also, the question asks about statements true for the school; this is a misrepresentation because we can't confirm this is a fixed 25% for the whole school from a single sample, and the option doesn't reference the sample. Eliminate B.

Step4: Evaluate Option C

Photography proportion: $\frac{11}{60}$. For 30 students: $\frac{11}{60} \times 30 = 11$. This holds. Keep C.

Step5: Evaluate Option D

No data on next year's enrollment. Eliminate D.

Step6: Evaluate Option E

Engineering proportion: $\frac{8}{60}$. For 120 students: $\frac{8}{60} \times 120 = 16$. This holds. Keep E.

Answer:

C. For every 30 students, about 11 take photography.
E. In a group of 120 students, about 16 likely take engineering.