27. The paper “Study on the Life Distribution of Microdrills”

(J. of Engr. Manufacture, 2002: 301–305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks)

when holes were drilled in a certain brass alloy.

11 14 20 23 31 36 39 44 47 50 59 61 65 67 68 71 74 76 78 79 81 84 85 89 91 93 96 99 101 104 105 105 112 118 123 136 139 141 148 158 161 168 184 206 248 263 289 322 388 513

a. Why can a frequency distribution not be based on the class intervals 0–50, 50–100, 100–150, and so on?

b. Construct a frequency distribution and histogram of the data using class boundaries 0, 50, 100, . . . , and then comment on interesting characteristics.

c. Construct a frequency distribution and histogram of the natural logarithms of the lifetime observations, and comment on interesting characteristics.

d. What proportion of the lifetime observations in this sample are less than 100? What proportion of the observations are at least 200?