Question

random students work from january 2016 regents
30 a statistics class surveyed some students during one lunch period to obtain opinions about television programming preferences. the results of the survey are summarized in the table below.
programming preferences
based on the sample, predict how many of the schools 351 males would prefer comedy. justify your answer.
let ( x=# ) males who prefer comedy
( \frac{x}{351}=\frac{70}{105}
ightarrow 105 x=\frac{24570}{105} )
( 105 x=24570 quad x=234 ) males

1. find the students mistake by comparing your work and this students work
2. using the rubric, how many points/credits would you give this student based on their work and why

Explanation:

Step1: Calculate the proportion of males who prefer comedy in the sample

The number of males in the sample is \(70 + 35=105\). The number of males who prefer comedy in the sample is \(70\). So the proportion \(p=\frac{70}{105}=\frac{2}{3}\)

Step2: Use the proportion to predict the number of males who prefer comedy in the school

Let \(x\) be the number of males who prefer comedy in the school. We know the total number of males in the school is \(N = 351\). Using the formula \(x=p\times N\), we substitute \(p=\frac{2}{3}\) and \(N = 351\). So \(x=\frac{2}{3}\times351 = 234\)

Step3: Analyze the student's work

The student set up the proportion \(\frac{x}{351}=\frac{70}{105}\) correctly. Cross - multiplying \(105x=70\times351\) (where \(70\times351 = 24570\)) and then solving for \(x\) by \(x=\frac{24570}{105}=234\) is also correct.

Answer:

1. The student's work is correct. They set up the proportion \(\frac{x}{351}=\frac{70}{105}\) (where \(x\) is the number of males who prefer comedy in the school of 351 males). Cross - multiplying gives \(105x=70\times351\). Solving for \(x\) gives \(x = 234\).
2. Assuming a typical rubric where setting up the proportion correctly (1 point) and solving for the variable correctly (1 point), the student would get 2 points. The student correctly identified the ratio of males who prefer comedy in the sample (\(\frac{70}{70 + 35}\)) and applied it to the total number of males in the school.