Question

A survey of 70 students from a high school is conducted. From this sample, it is found that 58 students have sent a text message on their smartphone at least once today, 21 have uploaded at least one "selfie" on their smartphone today, and 12 have done both.

Text Message Have Not Sent a Text Message Total
Have Taken a Selfie 12                                        21
Have Not Taken a Selfie 
Total 58                                                                 70




Complete the rest of the two-way frequency table above. Part A: How many students have neither sent a text message nor taken a selfie today? Part B: What percentage of students in the school (rounded to the nearest whole percent) have sent a text message or have taken a selfie at least once today?

Answer 1

Number of students who have sent a text message only is given by the difference between those that have sent a text message and those that have done both.
i.e. Number of students who has sent a text message only = 58 - 12 = 46

Number of students who have uploaded a selfie only is given by the difference between those that have uploaded a selfie and those that have done both.
i.e. Number of students who have uploaded a selfie only = 21 - 12 = 9

The total number of students surveyed is 70.
Let the number of students who have neither sent a text message nor taken a selfie today be x, then
46 + 9 + 12 + x = 70
67 + x = 70
x = 70 - 67 = 3

Therefore, 3 students neither sent a text message nor taken a selfie today.

The number of students that have sent a text message or have taken a selfie today is given by the sum of the number of students that have sent a text message and the number of students that have taken a selfie less the number of people that have done both.
i.e. number of students that have sent a text message or have taken a selfie today = 58 + 21 - 12 = 67.