Question

mr. mcelroy enjoys listening to his mp3 player, which has 2,000 songs in five different genres of music. he took a sample of the number of each type of song it played on two different one - hour sessions when it was set to play a random mix. the counts are shown in the table below. which proportion would predict the number of jazz songs he has stored on his mp3 player? listening samples from mr. mcelroy’s mp3 player. sample 1: country 5, pop 4, classical 3, jazz 2, rock 6. sample 2: country 3, pop 3, classical 5, jazz 4, rock 5.

Explanation:

Step1: Sum total sample jazz songs

Add jazz counts from both samples: $2 + 4 = 6$

Step2: Sum total sample songs

Add all counts from both samples:
$(5+4+3+2+6) + (3+3+5+4+5) = 20 + 20 = 40$

Step3: Set up prediction proportion

Let $x$ = total jazz songs. The proportion uses the sample ratio of jazz to total songs, applied to the 2000 total songs:
$\frac{\text{Total Sample Jazz}}{\text{Total Sample Songs}} = \frac{x}{\text{Total MP3 Songs}}$
$\frac{6}{40} = \frac{x}{2000}$

Answer:

The proportion $\boldsymbol{\frac{6}{40} = \frac{x}{2000}}$ (or simplified $\boldsymbol{\frac{3}{20} = \frac{x}{2000}}$) predicts the number of jazz songs, where $x$ is the total number of jazz songs on the MP3 player. Solving gives $x=300$ jazz songs.