The article “Study on the Life Distribution ofMicrodrills” (J. of Engr. Manufacture, 2002: 301–305) reported the following observations, listed inincreasing order, on drill lifetime (number of holesthat a drill machines before it breaks) when holes weredrilled in a certain brass alloy. 59 61 65 67 68 71 74 76 78 7981 84 85 89 91 93 96 99 101 104105 105 112 118 123 136 139 141 148 158161 168 184 206 248 263 289 322 388 513a. Why can a frequency distribution not be based onthe class intervals 0–50, 50–100, 100–150, andso on?b. Construct a frequency distribution and histogram ofthe data using class boundaries 0, 50, 100, … , andthen comment on interesting characteristics.c. Construct a frequency distribution and histogram ofthe natural logarithms of the lifetime observations,and comment on interesting characteristics.d. What proportion of the lifetime observations in thissample are less than 100? What proportion of theobservations are at least 200?
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.
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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