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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) $411$

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Experimental probability

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 estimate the number of students whose favorite season is summer based on the sample.
Calculate proportion of students who chose summer: Calculate the proportion of students in the sample who chose summer as their favorite season. $\newline$ Proportion of students who chose summer $= \frac{\text{Number of students who chose summer}}{\text{Number of students surveyed}}$ $\newline$ $= \frac{31}{57}$
Estimate number of students who prefer summer: 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 prefer summer $= \frac{\text{Proportion of students who chose summer}}{\text{Total number of students at Sunnydale High}}$ $\newline$ $= \left(\frac{31}{57}\right) * 721$
Perform calculation to find estimate: Perform the calculation to find the estimate. $\newline$ Estimated number of students who prefer summer = $(31 / 57) \times 721$ $\newline$ = $0.543859649 \times 721$ $\newline$ $\approx 392$ (rounded to the nearest whole number)

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