Statistics Solutions

(See Steps) BROAD CASTING. An all-news radio station has made a survey of the listening habits of local residents between the hours of 5:00 RM. and mid-

Question: BROAD CASTING. An all-news radio station has made a survey of the listening habits of local residents between the hours of 5:00 RM. and mid- night. The survey indicates that the percentage of the local adult population that is tuned in to the station \(x\) hours after 5:00 P.M. is

\[f(x)=\frac{1}{8}\left(-2 x^{3}+27 x^{2}-108 x+240\right)\]
  1. At what time between 5:00 P.M. and midnight are the most people listening to the station? What percentage of the population is listening at this time?
  2. At what time between 5:00 P.M. and midnight are the fewest people listening? What percentage of the population is listening at this time?

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