Question

a group of 120 people were asked whether their income level is above or below $25,000 and whether they subscribe to a movie channel. the data from the survey is shown in the venn diagram. use the venn diagram to find the missing values in the frequency table. which shows the correct values for the variables in the table? a = 18, b = 34, c = 65 a = 34, b = 18, c = 68 a = 34, b = 68, c = 47 a = 47, b = 18, c = 68

Explanation:

Step1: Find the value of \(a\)

The value of \(a\) is the number of people who are subscribers but not below \(\$25,000\). From the Venn - diagram, this is \(34\).

Step2: Find the value of \(b\)

The value of \(b\) is the number of people who are both below \(\$25,000\) and subscribers. From the Venn - diagram, this is \(18\).

Step3: Find the value of \(c\)

The value of \(c\) is the total number of subscribers. We use the formula \(n(\text{subscribers})=a + b\). Substituting \(a = 34\) and \(b = 18\), we get \(c=a + b=34+18 = 52\) (This is wrong. Wait, no. Wait, actually, the total number of people is \(120\). The number of people below \(\$25,000\) only is \(55\), both is \(18\), subscribers only is \(34\), and non - subscribers and non - below \(\$25,000\) is \(13\). The number of subscribers \(c\) is \(18 + 34=52\) (wrong approach). Wait, no. Wait, in the frequency - table context (assuming the table columns are for subscription status). Wait, no, re - check.

Wait, actually, if we assume the table rows and columns: Let's re - think. The number of people above \(\$25,000\): non - subscribers (only) is \(13\), subscribers (only) is \(34\). The number of people below \(\$25,000\): non - subscribers is \(55\), subscribers is \(18\).

The number of subscribers \(c\): \(18+34 = 52\) (wrong). Wait, no, wait the options. Wait, another approach:

The value of \(a\): from the Venn - diagram, the part of the "subscriber" circle that does not overlap with the "below \(\$25,000\)" circle is \(34\), so \(a = 34\).

The value of \(b\): the overlapping part (subscriber and below \(\$25,000\)) is \(18\), so \(b = 18\).

The value of \(c\): the total number of subscribers is \(34 + 18=52\) (wrong). Wait, no, wait the total number of people is \(120\). The number of people below \(\$25,000\) is \(55 + 18=73\), above \(\$25,000\) is \(34+13 = 47\). But if we consider the table (assuming columns are for income and rows for subscription). Wait, no, looking at the options.

Wait, if \(a\) is the number of subscribers above \(\$25,000\) (\(34\)), \(b\) is the number of subscribers below \(\$25,000\) (\(18\)), and \(c\) is the total number of subscribers \(34 + 18=52\) (not in options). Wait, no, re - check the problem.

Wait, no, maybe mis - interpreting the Venn - diagram. The rectangle has \(120\) people. The "below \(\$25,000\)" circle: \(55+18\), the "subscriber" circle: \(18 + 34\). The number of people above \(\$25,000\) and non - subscribers is \(13\).

If the table is:

	Above	Below
Non - Subscriber	\(13\)	\(55\)

The total number of people \(120\). The number of subscribers \(a + b\), non - subscribers \(13 + 55=68\). The total number of people \( (a + b)+(13 + 55)=120\).

Since \(a = 34\) (subscribers above \(\$25,000\)), \(b = 18\) (subscribers below \(\$25,000\)), then the number of non - subscribers \(c=13 + 55 = 68\)

Answer:

\(a = 34,b = 18,c = 68\)