To determine which statement is true you have to calculate each proportion:
A. Statement "About a fourth of the students prefer small screens."
You have to determine the proportion of students that prefer small screens:
[tex]P(Small|Student)=\frac{nºstudents\text{ that like small scr}eens}{nº\text{ students }}[/tex]Nº of students that prefer small screens: 48
Nº students surveyed: 100
[tex]P(\text{Small}|S\text{tudents)}=\frac{48}{100}=0.48[/tex]About half the students prefer small screens. This statement is false.
B. Statement "Most of the people surveyed were adults."
To check this statement you have to determine the proportion of adults surveyed:
[tex]P(\text{Adults)}=\frac{nº\text{adults}}{\text{total people}}[/tex]Nº adults surveyed: 100
Total people surveyed: 200
[tex]P(\text{Adults)}=\frac{100}{200}=0.50[/tex]Half of the people surveyed were adults. This statement is false.
C. Statement: "Most of the adults prefer a large screen size."
To determine if this statement is true, you have to calculate the proportion of adults that prefer a large screen size:
[tex]P(\text{LargeScreen}|\text{Adult)}=\frac{nº\text{adults that like large scre}ens}{nº\text{ adults}}[/tex]Nº adults that like large screens: 82
Nº adults surveyed: 100
[tex]P(\text{LargeScreen}|\text{Adult)}=\frac{82}{100}=0.82[/tex]82% of the adults prefer large screens. This statement is true.
D. Statement "Most of the people surveyed prefer a small screen size."
To determine if this statement is true, you have to calculate the proportion of people that preferred small screens:
[tex]P(\text{Small)}=\frac{nº\text{people that prefer small scre}ens}{Total}[/tex]Nº of people that prefer small screens: 66
Nº of people surveyed: 200
[tex]P(\text{Small)}=\frac{66}{200}=0.33[/tex]33% of the people surveyed preferred small screens. This statement is false.
Statement C is true.
