For this data analysis, we will look at the song length (in seconds) for a sample of 300 songs, and we will try to determine if the song length is approximately normally distributed. Step 1: Below is a frequency distribution. Complete the table by filling in the relative frequency. State the relative frequencies as percents rounded to 1 decimal place. Song Length (seconds) Frequency Relative Frequency 0-59 5 1.7% 60-119 29 9.7% 120-179 69 23% 180-239 94 31.3% 240-299 70 23.3% 300-359 28 9.3% 360-419 5 1.7% Total 300 100% What is the probability that a randomly selected song is between 3 and 5 minutes (between 180 seconds and 299 seconds)? State your answer as a percent rounded to 1 decimal place. Mean=42.9, STD= 34.92 Between 180 and 299= 0.0 Step 2: Below is the histogram for the data above. Based on a visual inspection of the data, does it appear to be normally distributed? Yes Step 3: Work with the sample data. State the mean (round to one decimal place) and standard deviation (round to two decimal places). Hint: For the mean, use =AVERAGE(D2:D301) and for the standard deviation, use =STDEV.S(D2:D301). Pick any song from the list and calculate the z-score for its length (round to 1 decimal place). State the song name, song length, and z-score. Explain what the z-score tells you about the song's length relative to the other songs in the sample. Step 4: Use the mean and standard deviation to label the normal distribution. Round to 1 decimal place. Define the random variable for the graph above. X= Step 4: Use the Empirical Rule to complete the table below. The X column is based on the normal distribution above, and n is the number of songs that fall into the range of values in the prior column. Here is how to interpret the first row: Songs between 137.6 seconds and 280.4 seconds are within one standard deviation of the mean. 212 songs in the sample are between 137.6 and 280.4 seconds. 70.7% of songs are within one standard deviation of the mean. Empirical Rule X n % of sample 68% 137.6300) How does P(180x<300) from above #9 compare to the probability that a randomly selected song is between 3 and 5 minutes that you found using the frequency distribution (#1)? Based on this does it seem reasonable to use the Empirical Rule (normalcdf) to calculate probabilities for song length? Submit: Upload a file that includes your answers to #1 - 11, normal distribution numbers, and completed table. Be sure to be thorough in your responses that require explanations. Your file may be a Word doc, PDF, or a PowerPoint. FOR STEP 3 YOU CAN SKIP IT