Question

a) there are a total of people in the survey
b) % of teenagers own an iphone.
c) % of teenagers an iphone or drive to school.
d) % of teenagers have an iphone and drive to school
e) % of teenagers do not have an iphone.
f) % of teenagers drive to school, but do not have an iphone

Explanation:

Step1: Calculate total number of people

Add all the numbers in the Venn - diagram and the universal set. \(35 + 45+40 + 20=140\)

Step2: Calculate percentage of iPhone owners

Number of iPhone owners \(n(A)=35 + 45=80\). Percentage \(=\frac{80}{140}\times100\approx57.1\%\)

Step3: Calculate percentage of iPhone or drive to school

Number of iPhone or drive to school \(n(A\cup B)=35 + 45+40 = 120\). Percentage \(=\frac{120}{140}\times100\approx85.7\%\)

Step4: Calculate percentage of iPhone and drive to school

Number of iPhone and drive to school \(n(A\cap B) = 45\). Percentage \(=\frac{45}{140}\times100\approx32.1\%\)

Step5: Calculate percentage of non - iPhone owners

Number of non - iPhone owners \(=40 + 20=60\). Percentage \(=\frac{60}{140}\times100\approx42.9\%\)

Step6: Calculate percentage of drive to school but no iPhone

Number of drive to school but no iPhone \(=40\). Percentage \(=\frac{40}{140}\times100\approx28.6\%\)

Answer:

a) \(140\)
b) \(57.1\%\)
c) \(85.7\%\)
d) \(32.1\%\)
e) \(42.9\%\)
f) \(28.6\%\)