Question

a group of 250 middle school students were asked whether they prefer playing video games or watching tv in their spare time. the genders of the students and their responses are reported in the following table.

	girls	boys
watching tv	102	38

(a) what percentage of the students prefer watching tv?
(b) what percentage of the students are boys?

Explanation:

Part (a)

Step1: Find total students who prefer watching TV

To find the number of students who prefer watching TV, we add the number of girls and boys who prefer watching TV. From the table, girls who prefer watching TV are 102 and boys are 38. So total students who prefer watching TV is \(102 + 38 = 140\).

Step2: Calculate the percentage

The total number of students is 250. The percentage of students who prefer watching TV is calculated as \(\frac{\text{Number of students who prefer watching TV}}{\text{Total number of students}}\times100=\frac{140}{250}\times100\). Simplifying \(\frac{140}{250}=\frac{14}{25}\), and \(\frac{14}{25}\times100 = 56\%\).

Step1: Find total number of boys

To find the total number of boys, we add the number of boys who prefer playing video games and watching TV. From the table, boys who prefer playing video games are 72 and watching TV are 38. So total number of boys is \(72+38 = 110\).

Step2: Calculate the percentage

The total number of students is 250. The percentage of boys is calculated as \(\frac{\text{Total number of boys}}{\text{Total number of students}}\times100=\frac{110}{250}\times100\). Simplifying \(\frac{110}{250}=\frac{11}{25}\), and \(\frac{11}{25}\times100 = 44\%\).

Answer:

\(56\%\)

Part (b)