3. (20 pts) Tim and Robel measure the distance that a toy Nerf gun can shoot a bullet when the gun is cocked at 45°.They make 10 measurements: 48.3, 50.1,

48.9, 49.2, 49.3, 51.5, 49.9, 49.2, 49.8, and 50.2 m. (a) Calculate the sample mean, sample standard deviation, median, and mode. Note: You may use Excel, but keep in mind that Excel will not be available on exams, so make sure you know how to calculate these statistical quantities"by hand" and/or with a calculator. (b) Compare Sturgis' rule and the Rice rule for this set of data. How many bins are "ideal" for a histogram of these data? (c) Use Excel to draw a histogram with the following four bins: 48 to 49, 49 to 50, 50 to 51, and 51 to 52. Make the histogram nice-looking, without gaps between bars. Are these enough data points to expect that deviations from the mean are nearly random? What do you expect would happen if Tim and Robel took many more data points?