Access the data about lengths of alternative rock songs, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website. At the start of this section, we analyzed the lengths of songs played on the alternative rock radio station Live 105. You will now analyze the lengths (in seconds) of all songs on albums by bands typically featured on Live 105. Some of the songs on the albums have been played on Live 105, but many have not.
a. Construct a relative frequency histogram of the song lengths, beginning with lower class limit 0 seconds and class width 50 seconds. Display the relative frequencies above the bars if the technology you are using has this feature.
b. Describe the shape of the distribution.
c. Compute the mean and the standard deviation.
d. Assuming the distribution is approximately normal, use the mean and the standard deviation you found in part (c) to estimate the proportion of song lengths that are between 200 seconds and 300 seconds.
e. Find the actual proportion of song lengths that are between 200 seconds and 300 seconds. Compare the result to the one you found in part (d). Does your comparison suggest that there are too few or too many observations near the mean for the distribution to be exactly normal? Explain.
f. Assuming the distribution is approximately normal, use the mean and the standard deviation you found in part (c) to estimate the proportion of song lengths that are between 100 seconds and 400 seconds. Then find the actual proportion of song lengths that are between 100 seconds and 400 seconds. Compare your two results.