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 7E.20 gives the dates of the 1989 homicides and the number of days between each homicide.

(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 more closely resemble data from a normal distribution? Is the plot very different from the one in part (b)?
(d) Construct an individuals control chart using the transformed data from part (b).
(e) Construct an individuals 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.

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TABLE 7E.20 Homicide Data from Waco, Texas, for Exercise 7.76 Days Days Month Date Between Month Date Betwees an. 20 Feh23 Feh 25 March 5 March 10 April 4 2 May May 24 May 28 June 7 June 6 9.25 Junc 6 0.50 June 22 5.25 June 25 July July July9 July 26 17 Sep. Sep. 22 13 Sep Oct. Oct Oct. 9 45 19 Nov.214 Nov. 25 23 Dec. 28 33 Dec. 29