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A preliminary study of the Jingdong black gibbon found that the mean song bout duration in...

A preliminary study of the Jingdong black gibbon found that the mean song bout duration in the wet season is 12.59 minutes with a variance of 28.2 minutes. Assuming that song bout is normally distributed, determine the percentage of songs that have durations within 1.5 standard deviations to either side of the mean.

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Answer #1

Let X denote the duration of the song (in minutes). Then

Now,

Thus 86.638% of songs have duration within 1.5 standard deviations to either side of the mean.

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