Kittlitz (1999) presents data on homicides in Waco, Texas, for the years 1980-1989 (data taken from the Waco Tribune-Herald, December 29, 1989). There were 29 homicides in 1989. Table 6E.15 gives the dates of the 1989 homicides and the number of days between each homicide. The asterisks refer to the fact that two homicides occurred on June 16 and were determined to have occurred 12 hours apart.

a. Plot the days-between-homicides data on a normal probability plot. Does the assumption of a normal distribution seem reasonable for these data?
b. Transform the data using the 0.2777 root of the data. Plot the transformed data on a normal probability plot. Does this plot indicate that the transformation has been successful in making the new data more closely resemble data from a normal distribution?
c. Transform the data using the fourth root (0.25) of the data. Plot the transformed data on a normal probability plot. Does this plot indicate that the transformation has been successful in making the new data resemble more closely data from a normal distribution? Is the plot very different from the one in part (b)?
d. Construct an individual control chart using the transformed data from part (b).
e. Construct an individual control chart using the transformed data from part (c). How similar is it to the one you constructed in part (d)?
f. Is the process stable? Provide a practical interpretation of the control chart.

(days (days Days Between) nth Date Between 0.2777 Days Between) DaysMonth Date Between Days Between etween 0.2777 20 July 1.212261 1.189207 an Feb. 23 34 2.6625132.414736 July Feb. 25 March 5 March 105 Api 4 25 2.444601 2.236068 Sep 24 2 1.212261 1.189207 2 1.212261 1.189207 July 26 17 2.19632 2.030543 9 45 2.878042 2.59002 1.563522 1.495349 Sep 2213 2.038647 1.898829 1.781509 1.681793 Sep 1.716658 1.626577 1.35674 1.316074 1.469576 1.414214 7 10 1.895396 1.778279 Oct 9 1.946233 1.82116 733 2.640531 2.396782 Oct 2.19632 2.030543 Oct 1.469576 1.414214 Oct May 24 17 May 28 4 June June 16 9.25 1.854802 1.743956 Nov. 2 14 2.081037 1.934336 June 16* 0.5 0.824905 0.840896 Nov 25 23 2.388646 2.189939 June 22 5.25 1.58485 June July 1.5137 Dec 28 33 2.640531 2.396782 1.35674 1.316074 Dec 29 6 11 1946233 1.82116