Struggling with concept on this Math problem

Question

IN a random sampling from a survey concerning music listening habits, 120 out of 180 mid-level executives preferred country to heavy metal. Taking all the data from the survey, 336 mid-level executives expressed a preference for country over heavy metal. How many mid-level executives took part in the survey?

Answer 1

Kevin, This problem depends on your knowing something about surveys And sampling.

The survey was given to a whole lot of music executives, let’s call that number m.

However, a sample (that is, some but not all) of the executives is also mentioned. Let’s call that number s.

Now we can translate the two sentences at the top.

(1) In a random sampling from a survey concerning music listening habits, 120 out of 180 mid-level executives preferred country to heavy metal.

This means that if we look at one group of s execs (where s = 180), only 120 preferred country to heavy metal.

(2) Taking all the data from the survey, 336 mid-level executives expressed a preference for country over heavy metal.

This means that when you look at the entire survey of m execs, only 336 of them preferred county to heavy metal.

So the question is: how many is m?

A reasonable way to estimate is to say that the ratio of country lovers to HM lovers is 120/180, and that it might be the same ratio for the whole survey:

336 / m

So solve this equation for m:

120 / 180 = 336 / m

Ill guess you know how to do this. If not, please ask.