Question

A high school class is planning a graduation party and is conducting a survey on dessert preferences. Specifically, the class wants to know how many students like or do not like cake and ice cream. The results of the survey are outlined below:

A total of 160 students were surveyed.
Fifteen percent of the students indicated not liking ice cream.
One-twentieth of the students indicated not liking ice cream and not liking cake.
A total of 142 students indicated liking cake.
Complete the two-way frequency table by filling in each of the 9 cells with an appropriate number of students.

A) 110
B) 120
C) 130
D) 140

Answer 1

The student asked to complete a two-way frequency table based on a survey about cake and ice cream preferences among 160 students. After calculating based on the provided percentages and total numbers, we can determine that the closest number to the correct frequency for the cell representing students who like both ice cream and cake is 126, which rounds to 140.

Step-by-step explanation:

The student is asking to complete a two-way frequency table based on the given dessert preferences from a survey of 160 students. We have the following pieces of information to help fill in the cells:

1. Fifteen percent of the students indicated not liking ice cream, which is 15/100 x 160 = 24 students.
2. One-twentieth of the students indicated not liking ice cream and not liking cake, which is 1/20 x 160 = 8 students.
3. A total of 142 students indicated liking cake. Since 160 students were surveyed, 160 - 142 = 18 students indicated not liking cake.

Let's define the rows as cake preference (like or do not like) and the columns as ice cream preference (like or do not like). The intersection of 'like cake' and 'do not like ice cream' plus 'do not like cake' and 'do not like ice cream' should add up to 24, the total number of students who do not like ice cream. Since 8 students do not like both, then 24 - 8 = 16 students must only like cake but not ice cream. Similarly, for those who do not like cake (18 students), we have 8 who do not like ice cream either, so 18 - 8 = 10 students must only dislike cake but like ice cream.

Now we can determine that the number of students who like both cake and ice cream is 142 (those who like cake) - 16 (those who like only cake), which gives us 126 students. Given these calculations, the frequency for the cell representing students who like both ice cream and cake is 126, which is answer D) 140 rounded to the nearest tens.