Question

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 1

Given that a residential community was polling households to find out whether they wanted to get their TV signal from a satellite or cable.

Given the results as shown in the Venn diagram with the number of people that want satellite = 55, the number of people that want cable = 75, the number of people that want both satellite and cable = 12 and the number of people that want neither satellite nor cable = 4.
Thus the total number of people polled is 146.

Recall that relative frequency is the ratio of the outcome of an event to the total possible outcomes (sometimes expressed as a percentage).

From the table, a is the relative frequency of the number of people that want satelite but not cable.
Thus,

`a= (55)/(146) =0.38=38\%`

From the table, b is the relative frequency of the number of people that want neither satelite nor cable.
Thus,

`b= (4)/(146) =0.03=3\%`

Therefore, the values of a and b in the relative frequency table for the survey results rounded to the nearest percent are a = 38%, b = 3%.