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3.31 The clearness index was determined for the skies over Baghdad for each of the 365 days during a particular year (“Contribution to the Study of the Solar Radiation Climate of the Baghdad Environment,” Solar Energy [1990]: 7–12). The accompanying table summarizes the resulting data:
Number of Days
|
Clearness Index (frequency)
a. Summarize these data in the form of a frequency dis- tribution, using class intervals of 0 to 6, 6 to 12, and so on.
b. Compute the relative frequencies and cumulative rela- tive 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 approx- imate 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?
a. Determine the relative frequencies and draw the corre-sponding histogram. (Be careful here—the intervals do not all have the same width.)
b. Cloudy days are those with a clearness index smaller than 0.35. What proportion of the days was cloudy?
c. Clear days are those for which the index is at least
0.65. What proportion of the days was clear?