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. $\newline$ Cordelia surveyed $57$ students, and $31$ of them chose summer as their favorite season. We need to estimate how many of the $721$ students at Sunnydale High would choose summer as their favorite season based on this sample.
Calculate Proportion: Calculate the proportion of students in the sample who chose summer as their favorite season. $\newline$ Proportion of students who chose summer = \frac{\text{Number of students who chose summer}}{\text{Total number of students surveyed}}$\newline= \frac{31}{57}$
Estimate Number of Students: Use the proportion to estimate the number of students in the entire school who would choose summer as their favorite season. $\newline$ Estimated number of students who choose summer $= \frac{31}{57} \times 721$
Perform Calculation: Perform the calculation to find the estimate. $\newline$ Estimated number of students who choose summer = $(31 / 57) * 721$ $\newline$ = $0.543859649 * 721$ $\newline$ $\approx 392.298245614$ (This is an estimate, so we round to the nearest whole number) $\newline$ $\approx 392$