Question

The clearness index was determined for the skies over Baghdad for each of the 365 days during a particular year. The following accompanying table summarizes the resulting data.

Clearness Index	Number of Days (frequency)
0.15 to <0.25	9
0.25 to <0.35	19
0.35 to <0.45	28
0.45 to <0.50	24
0.50 to <0.55	39
0.55 to <0.60	52
0.60 to <0.65	96
0.65 to <0.70	87
0.70 to <0.75	11

(a) Determine the relative frequencies and fill in the following table. (Round your answer to five decimal places if needed.)

Class Intervals	Frequency	Rel. Frequency
0.15 to <0.25	9
0.25 to <0.35	19
0.35 to <0.45	28
0.45 to <0.50	24
0.50 to <0.55	39
0.55 to <0.60	52
0.60 to <0.65	96
0.65 to <0.70	87
0.70 to <0.75	11

(b) Draw the histogram. (Be careful here-the intervals do not all have the same width. Do this on paper. Your instructor may ask you to turn in this graph.)

(c) Cloudy days are those with a clearness index smaller than 0.35. What proportion p of the days was cloudy? (Round your answer to two decimal places if needed.)
p =

(d) Clear days are those for which the index is at least 0.65. What proportion p of the days was clear? (Round your answer to two decimal places if needed.)
p =

2)  

The paper "Lessons from Pacemaker Implantations" 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 summarized in the table below.

20	14	8	25	22	26	29	8	17	28	22	25
6	22	15	20	17	8	20	22	15	24	14	13
11	6	30	22	27	14	24	7	15	6	14	27
15	29	25	18	17	7	19	24	9	13	27	20
8	18	28	17	16	26	22	19	6	7	9	22
17	27	29	26	4	28	3	12	16	9	32	29
32	24	26	20	20	18	13	13	15	23	35	35
12	35	28	22	33

(a) Fill in the following table. (Round your answer to four decimal places if needed.)

Classes	Frequency	Relative Frequency	Cumulative Relative Frequency
0 - <6
6 - <12
12 - <18
18 - <24
24 - <30
30 - <36

(b) Use the cumulative relative frequencies to give approximate answers to the following questions. (Round your answer to four decimal places if needed.)

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

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?
p =

(c) Construct a cumulative relative frequency plot. Prepare an Excel document. The file should be named with a .xls extension.
Use it to answer the following questions. (Round your answers to the nearest whole number if needed.)

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

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

Answer 1