Bounce Club surveyed a random sample of $55$ of their members about their favorite type of music. Of the members surveyed, $22$ said that jazz is their favorite type of music. There are $422$ Bounce Club members. $\newline$ Based on the data, what is the most reasonable estimate for the number of Bounce Club members whose favorite type of music is jazz music? $\newline$ Choose $1$ answer: $\newline$ (A) $22$ $\newline$ (B) $141$ $\newline$ (C) $\mathbf{1 6 9}$ $\newline$ (D) $253$

Full solution

Q. Bounce Club surveyed a random sample of

55

of their members about their favorite type of music. Of the members surveyed,

22

said that jazz is their favorite type of music. There are

422

Bounce Club members.

\newline

Based on the data, what is the most reasonable estimate for the number of Bounce Club members whose favorite type of music is jazz music?

\newline

Choose

1

answer:

\newline

(A)

22

\newline

(B)

141

\newline

(C)

\mathbf{1 6 9}

\newline

(D)

253

Total Surveyed Members: Total members surveyed: $55$ $\newline$ Members who prefer jazz: $22$ $\newline$ Total Bounce Club members: $422$ $\newline$ Calculate the proportion of surveyed members who prefer jazz. $\newline$ Proportion = (Members who prefer jazz) / (Total members surveyed) $\newline$ Proportion = $22 / 55$
Calculate Proportion: Perform the calculation for the proportion. $\newline$ Proportion = $\frac{22}{55} = 0.4$
Calculate Proportion: Use the proportion to estimate the total number of club members who prefer jazz. $\newline$ Estimated number $=$ Proportion $*$ Total Bounce Club members $\newline$ Estimated number $= 0.4 \times 422$
Estimate Club Members: Perform the calculation for the estimated number. $\newline$ Estimated number = $0.4 \times 422 = 168.8$ $\newline$ Since we can't have a fraction of a person, round to the nearest whole number.
Round Estimated Number: Round the estimated number to the nearest whole number. $\newline$ Estimated number $\approx 169$