The paper “Lessons from Pacemaker Implantations” (Journal of the American Medical Association [1965]: 231– 232) gave the results of a study that followed 89 heart patients who had received electronic pacemakers. The time (in months) to the first electrical malfunction of the pacemaker was recorded:

24 20 16 32 14 22 2 12 24 6 10 20 8 16 12 24 14 20 18 14 16 18 20 22 24 26 28 18 14 10 12 24 6 12 18 16 34 18 20 22 24 26 18 2 18 12 12 8 24 10 14 16 22 24 22 20 24 28 20 22 26 20 6 14 16 18 24 18 16 6 16 10 14 18 24 22 28 24 30 34 26 24 22 28 30 22 24 22 328

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 interval 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 first year?

ii. If the pacemaker must be replaced as soon as the first 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?