a residential community was polling households to find out whether they wanted to get their tv signal from a…

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%

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%

Answer

Explanation:

Step1: Calculate total number of households

$55 + 12+75 + 4=146$

Step2: Calculate value of $a$ (relative - frequency of preferring satellite)

The number of households preferring satellite is $55 + 12=67$. The relative - frequency $a=\frac{67}{146}\times100%\approx46%$ (This step is wrong, let's correct it. The correct way to calculate $a$ is the proportion of those who prefer satellite only or both satellite and cable among all non - cable - only people. The number of non - cable - only people is $55 + 12+4 = 71$. The number of people who prefer satellite (satellite only or both) is $55 + 12=67$. So $a=\frac{67}{71}\times100%\approx93%$)

Step3: Calculate value of $b$ (relative - frequency of preferring neither)

The number of households preferring neither is $4$. The relative - frequency $b = \frac{4}{146}\times100%\approx3%$

Answer:

$a = 93%, b = 3%$