Question

lesson
two - way tables
lets look at categorical data.
warm - up utensils and paper preferences
several students are surveyed about whether they prefer writing with a pen or a pencil, and they are also asked whether they prefer lined paper or unlined paper. some of the results are:
the survey included 100 different students.
40 students said they prefer using a pen more than a pencil.
45 students said they prefer using unlined paper more than lined paper.
10 students said they prefer lined paper and a pen.
45 students said they prefer a pencil and lined paper.
for each part, explain or show your reasoning.
1 how many students prefer using pencil more than pen?
2 how many students prefer using pen and unlined paper?
3 how many students prefer using pencil and unlined paper?

Explanation:

Step1: Calculate students preferring pencil more

We know total students = 100. 40 students prefer pen more. So students preferring pencil more = 100 - 40 = 60.

Step2: Calculate students preferring pen and un - lined paper

We know 45 prefer un - lined paper more and 10 prefer lined paper and pencil. Also 45 prefer lined paper and pen. Let \(x\) be students preferring pen and un - lined paper. Let \(y\) be students preferring pencil and un - lined paper. We have \(x + y=45\) and total students = 100. Since 10 + 45=55 students are accounted for in lined - paper cases. So students preferring pen and un - lined paper \(x=45-(100-(10 + 45))=0\).

Step3: Calculate students preferring pencil and un - lined paper

Since 45 students prefer un - lined paper more and 0 prefer pen and un - lined paper, students preferring pencil and un - lined paper is 45.

Answer:

1. 60
2. 0
3. 45