The article "Determination of Most Representative Subdivision" ( Journal of Energy Engineering [1993]: 43-55) gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or under- ground lines. Data on the variable x = total length of streets within a subdivision are as follows:

a. Summarize these data in the form of a frequency distribution, using class intervals of 0 to 6, 6 to 12, and so on.

b. Compute the relative frequencies and cumulative relative frequencies for each class interval of the frequency distribution of Part (a).

c. Show how the relative frequency for the class inter- val 12 to 18 could be obtained from the cumulative relative frequencies.

d. Use the cumulative relative frequencies to give approximate answers to the following:

i. What proportion of those who participated in the study had pacemakers that did not malfunction within the ?rst year?

ii. If the pacemaker must be replaced as soon as the ?rst electrical malfunction occurs, approximately what proportion required replacement between 1 and 2 years after implantation?

e. Construct a cumulative relative frequency plot, and use it to answer the following questions.

i. What is the approximate time at which about 50% of the pacemakers had failed?

ii. What is the approximate time at which only about 10% of the pacemakers initially implanted were still functioning?