(a) What percent of the people surveyed owned a cell phone? (b) What percent of the people surveyed owned only a cell phone?

Question

A consumer survey was conducted to examine patterns in ownership of tablet computers, cellular telephones, and Blu-ray players. The following data were obtained: 317 people had tablet computers, 236 had cell phones, 267 had Blu-ray players, 69 had all three, 64 had none, 96 had cell phones and Blu-ray players, 57 had cell phones but no computers or Blu-ray players, and 108 had computers and Blu-ray players but no cell phones. (Round your answers to one decimal place.)

Answer 1

I will round to the nearest percentage.

Always first be clear on what is being asked or required:

(REQUIRED1) What percent of the people surveyed owned a cell phone?

(REQUIRED2) What percent of the people surveyed owned only a cell phone?

The three pieces of information you need to solve this is are:

people who own a cell phone,

people who own only a cell phone,

and total people surveyed.

With these three pieces of information you can calculate the two required answers.

Hint: I like to use Excel for this, as it allows me to use the functionality to filter columns and other Excel functionality that not only makes this easier but also helps avoid making mistakes that one is prone to make when using paper and pencil, but this certainly does not require a spreadsheet.

STEP 1:

Build a “truth table” and label the rows “scenarios” a to h

tablet computers cell phones blue-rays scenario

Y Y Y a

Y Y N b

Y N Y c

Y N N d

N Y Y e

N Y N f

N N Y g

N N N h

These are all possible combinations.

Note it is key that you derive total people surveyed.

Total people surveyed = a+b+c+d+e+f+g+h.

Four of the scenarios are provided in the problem.

tablet computers cell phones blue-rays scenario

Y Y Y a : 69 had all three

Y N Y c : 108 had computers and Blu-ray players but no cell phones

N Y N f : 57 had cell phones but no computers or Blu-ray players

N N N h : 64 had none

Scenario e = 96-69. If 96 had cell phones and Blu-ray players and 69 had all three, the difference is scenario e [cell phones and blue-rays but no tablet computers].

We are left with 3 scenarios (3 variables) and 3 equations, so we are in good shape

317 people had tablet computers

a + b + c + d = 317

236 had cell phones

a + b + e + f = 236

267 had Blu-ray players

a + c + e + g = 267

Plug in the scenarios that you know:

69 + b + 108 + d = 317

69 + b + 27 + 57 = 236

69 + 108 + 27 + g = 267

Simplify:

b + d = 317 - 69 - 108

b = 236 - 69 - 27 - 57

g = 267 - 69 - 108 - 27

Simplify:

b + d = 140

b = 83

g = 63

Thus d = 140-83= 57

Now that you have all your scenarios a through h then total surveyed = a+b+c+d+e+f+g+h = 528

a + b + e +f are those that have cell phones = 236

(REQUIRED1) What percent of the people surveyed owned a cell phone? = 236/528= 45%

(REQUIRED2) What percent of the people surveyed owned only a cell phone? Scenario f divided by 528 =11%

IMPORTANT: Don’t stop there. Always check your work, we have

tablets cell phones blue-ray identifier count

Y Y Y a 69

Y Y N b 83

Y N Y c 108

Y N N d 57

N Y Y e 27

N Y N f 57

N N Y g 63

N N N h 64

Go through all your statements and made sure you can prove them to be correct

317 people had tablet computers, yes

236 had cell phones, yes

267 had Blu-ray players, yes

69 had all three, yes

64 had none, yes

96 had cell phones and Blu-ray players, yes

57 had cell phones but no computers or Blu-ray players, yes

and 108 had computers and Blu-ray players but no cell phones. yes

If any of the statements given do not agree to your “truth table” don’t give up, redo the problem, we all make mistakes. Redo your work until your work checks.