The article “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?

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The article “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?

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Just part d. Not a through c. 

 

The article “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?

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