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A student suspects that the length of songs currently on her Spotify playlist are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-The symmetric middle 90% of songs have lengths between what two values? Round all values to one decimal place.
A) 155.0 seconds and 359.0 seconds
B) 151.0 seconds and 363.0 seconds
C) 149.0 seconds and 365.0 seconds
D) 153.0 seconds and 361.0 seconds

Question

Quizplus · Accepted Answer

The middle 90% of songs have lengths between 155.0 seconds and 359.0 seconds. This is because the mean is 257 seconds and the standard deviation is 62 seconds, so the z-scores for the 5th and 95th percentiles are -1.645 and 1.645, respectively. Multiplying these z-scores by the standard deviation and adding the mean gives the corresponding lengths.

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