Cordelia surveyed a random sample of $57$ students at Sunnydale High about their favorite season. Of the students surveyed, $31$ chose summer as their favorite season. If there are $721$ students at Sunnydale High, what is the most reasonable estimate of the number of students whose favorite season is summer? $\newline$ Choose $1$ answer: $\newline$ (A) $224$ $\newline$ (B) $329$ $\newline$ (C) $392$ $\newline$ (D) $411$

Full solution

Q. Cordelia surveyed a random sample of

57

students at Sunnydale High about their favorite season. Of the students surveyed,

31

chose summer as their favorite season. If there are

721

students at Sunnydale High, what is the most reasonable estimate of the number of students whose favorite season is summer?

\newline

Choose

1

answer:

\newline

(A)

224

\newline

(B)

329

\newline

(C)

392

\newline

(D)

411

Identify Given Information: Identify the given information and what we need to find. $\newline$ We are given: $\newline$ - Number of students surveyed = $57$ $\newline$ - Number of students who chose summer = $31$ $\newline$ - Total number of students at Sunnydale High = $721$ $\newline$ We need to find the most reasonable estimate of the number of students whose favorite season is summer.
Calculate Proportion: Calculate the proportion of students who chose summer as their favorite season from the survey. $\newline$ Proportion of students who chose summer $= \frac{\text{Number of students who chose summer}}{\text{Number of students surveyed}}$ $\newline$ $= \frac{31}{57}$
Estimate Number of Students: Use the proportion to estimate the number of students at Sunnydale High whose favorite season is summer. $\newline$ Estimated number of students who prefer summer $= \frac{31}{57} \times 721$
Perform Calculation: Perform the calculation to find the estimate. $\newline$ Estimated number of students who prefer summer = $(31 / 57) \times 721$ $\newline$ = $0.543859649 \times 721$ $\newline$ $\approx 392.1052632$
Round Estimate: Round the estimate to the nearest whole number, as we cannot have a fraction of a student. $\newline$ Estimated number of students who prefer summer $\approx 392$
Choose Closest Answer: Choose the closest answer from the given options. $\newline$ The closest answer to our estimate is $(C) 392$ .