Since the standard deviation is 2 songs, then, a student that likes more than 10 songs falls more than 1 standard deviation from the mean of 8 songs.
The region that corresponds to that situation is highlighted in the following diagram:
Add the percentages of that region to find the answer:
[tex]13.5+2.35+0.15=16[/tex]
Therefore, the probability that an individual student likes more than 10 songs is 16%.
4 songs is 2 standard deviations less than the mean of 8 songs, and 12 songs is 2 standard deviations more than the mean of 8 songs. The region that corresponds to that situation is highlighted in the following diagram:
Add the percentages of that region to find the answer:
[tex]13.5+34+34+13.5=95[/tex]
Therefore, the probability that an individual student likes between 4 and 12 songs is 95%.
