In Example 5, we analyzed the lengths of songs played on the alternative rock radio station Live 105. The lengths (in seconds) of all songs on albums by bands typically featured on Live 105 are described by the histogram in Fig. 76 and the information in Fig. 77. Some of the songs on the albums have been played on Live 105, but many have not.
Fig. 76

Fig. 77

a. Explain why the Empirical Rule can be applied.
b. What interval contains approximately 95% of the song lengths?
c. Would the interval you found in part (b) contain 95% of the song lengths of all types of music? Explain.
d. In Example 5, we found that songs played on Live 105 have a mean length of 232.9 seconds and standard deviation 49.6 seconds. By comparing these values to the mean and standard deviation of song lengths described in Fig. 77, explain why this suggests that the radio station does not tend to play songs that are too short or too long.
e. In Example 5, we found that 95% of the songs played on Live 105 have lengths that lie in the interval (133.7, 332.1). Is the interval wider or narrower than the interval you found in part (b)? What does this mean? How does this tie in with your explanation in part (d)?

Transcribed Image Text:

Lengths of Songs 140 120 100 80 60 40 20 100 200 300 400 500 600 Seconds Summary statistics: Column n MeanStd. dev Time 398253.09045 74.579911