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Probability and Statistics for Engineers Exercises

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Probability and Statistics for Engineers
Summer 2019 - 2020
Assignment # 1
Due: Wednesday 06-Aug-2020
Q. No. 1: The following data represent the length of tire life, in years, of 40 tires
17
20
10
9
23
13
12
19
18
24
12
14
6
9
13
6
7
10
13
7
13
7
18
7
10
4
27
19
16
8
7
10
5
14
15
10
9
6
7
15
(a)
Construct a frequency and relative frequency distributions, using 8 classes.
(b)
Find mean, median and mode for the life span of tires, using grouped data.
(c)
Also construct the frequency histogram and comment on the data.
Q. No. 2: The following are the numbers of minutes that a person had to wait for a bus to work
on 20 working days:
2
11
8
10
1
13
9
5
9
2
10
3
8
6
17
2
10
15
14
5
(a)
Find the mean, median and mode of the ungrouped data and comment on the data
behavior using measures of central tendency.
(b)
Find the highest possible measure of dispersion of the data, i.e. the Range.
(c)
Find inter-quartile range of the data.
(d)
Find inter-fractile range using 1/3 and 2/3 fractiles.

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Q.No. 3: The lengths of the power failure, in minutes, are recorded in the following table.
135
90
69
102
28
120
22
112
74
103
21
21
87
115
28
37
118
74
83
95
(a)
Find variance and standard deviation of the power failure times and comment on the data.
Q. No. 4: A tire manufacturer wants to determine the inner diameter of a certain grade of tire.
Ideally the diameter would be 570 mm. The data are as follows:
572
572
573
568
569
575
565
570
(a)
Find the sample mean and median.
(b)
Find the sample variance, standard deviation, and range.
(c)
Using the calculated statistics in parts (a) and (b), comment on the quality of the tires?
Q. No. 5: The lifetimes of electric bulbs for Company A and Company B are recorded in hours
as follows:
A
72
68
53
68
76
71
69
68
70
B
72
76
68
65
68
72
70
79
78
(a)
Find the variance and standard deviation for Company-A and Company-B.
(b)
Comment on the quality of the bulbs and suggest which one is better. (Use measures of
Variations).
-------------------------------------------------- Have Fun ----------------------------------------------

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Probability and Statistics for Engineers Summer 2019 - 2020 Assignment # 1 Due: Wednesday 06-Aug-2020 Q. No. 1: The following data represent the length of tire life, in years, of 40 tires 17 20 10 9 23 13 12 19 18 24 12 14 6 9 13 6 7 10 13 7 13 7 18 7 10 4 27 19 16 8 7 10 5 14 15 10 9 6 7 15 (a) Construct a frequency and relative frequency distributions, using 8 classes. (b) Find mean, median and mode for the life span of tires, using grouped data. (c) Also construct the frequency histogram and comment on the data. Q. No. 2: The following are the numbers of minutes that a person had to wait for a bus to work on 20 working days: 2 11 8 10 1 13 9 5 9 2 10 3 8 6 17 2 10 15 14 5 (a) Find the mean, median and mode of the ungrouped data and comment on the data behavior using measures of central tendency. (b) Find the highest possible measure of dispersion of the data, i.e. the Range. (c) Find inter-quartile range of the data. (d) Find inter-fractile range using 1/3 and 2/3 fractiles. Q.No. 3: The lengths of the power failure, in minutes, are recorded in the following table. 22 18 135 15 90 78 69 98 102 83 55 28 121 120 13 22 124 112 70 68 74 89 103 24 21 112 21 40 98 87 132 115 21 28 43 37 50 96 118 158 74 78 83 93 95 (a) Find variance and standard deviation of the power failure times and comment on the data. Q. No. 4: A tire manufacturer wants to determine the inner diameter ...
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