Question

Below is a cumulative relative frequency graph for the lengths, In minutes, or 200 songs recorded by The Rolling Stones.


Approximately what percent of the songs will last more than 7 minutes?


State the percentile for a song lasting 3 minutes interpret this value in the context of the problem.

Answer 1

Based on the plot of the Cummulative relative frequency graph shown ;

• Songs lasting more than 7 minutes is 2.5%

• The percentile of song lasting 3 minutes is the 30th percentile. This means 30% of the songs have a length of 3 minutes.

Using the Cummulative relative frequency curve, the location of the song length at 7 minutes on the curve corresponds to approximately 0.975 on the y - axis.

Hence, (1 - 0.975)% = 2.50%

The point at which song length equals 3 minutes has a corresponding value of 0.3 on the y - axis which is (0.3 × 100%) = 30% = 30th percentile

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