Question

a residential community was polling households to find out whether they wanted to get their tv signal from a satellite or cable. the results are shown in the venn diagram. what are the values of a and b in the relative - frequency table for the survey results? round answers to the nearest percent. a = 82%, b = 3% a = 38%, b = 50% a = 38%, b = 3% a = 93%, b = 19%

Explanation:

Step1: Calculate total number of households

$55 + 12+75 + 4=146$

Step2: Calculate value of a (percentage of those who prefer satellite)

Those who prefer satellite are $55 + 12=67$. So $a=\frac{67}{146}\times100\%\approx 45.89\% \approx 46\%$ (not in options, let's assume it's the percentage of those who prefer only - satellite). If we consider those who prefer satellite - related (satellite or both), $a=\frac{55 + 12}{146}\times 100\%\approx45.89\%\approx46\%$. If we calculate the percentage of those who prefer only satellite out of all non - cable - only households: non - cable - only households are $55+12 + 4=71$, and only satellite households are $55$. So $a=\frac{55}{71}\times 100\%\approx77.46\%\approx77\%$ (still not in options). Let's calculate the percentage of those who prefer satellite or both out of all households: $a=\frac{55 + 12}{55+12 + 75+4}\times100\%=\frac{67}{146}\times100\%\approx 45.89\%\approx46\%$. If we assume it's the percentage of those who prefer satellite or both out of all non - cable - only households: non - cable - only households are $55 + 12+4 = 71$, and satellite or both are $55 + 12=67$, $a=\frac{67}{71}\times100\%\approx94.37\%\approx94\%$ (not in options). Let's calculate the percentage of those who prefer only satellite out of all households: $a=\frac{55}{146}\times100\%\approx37.67\%\approx38\%$.

Step3: Calculate value of b (percentage of those who prefer neither)

$b=\frac{4}{146}\times 100\%\approx2.74\%\approx3\%$

Answer:

C. $a = 38\%, b = 3\%$