Question

The length of pop music songs is normally distributed with meze length of 215 seconds and a szard
deviation of 38 seconds. What percent of pop songs have lengths between three and four minutes?
(1) 48%
(3) 61%
(2) 57%
(4) 67%

Answer 1

58% of pop songs have lengths between three and four minutes

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score, \mu=mean,\sigma=standard \ deviation\\\\Given\ that:\\\\\mu=215,\sigma=38.\\\\For\ x=3\ min(180\ sec):\\\\z=\frac{180-215}{38}=-0.92\\\\For\ x=4\ min(240\ sec):\\\\z=\frac{240-215}{38}=0.71$

From the normal distribution table, P(180 < x < 240) = P(-0.92 < z < 0.71) = P(z < 0.71) - P(z < -0.92) = 0.7611 - 0.1788 = 0.5823 = 58%

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