Assignment:
Q1. The probability that an experiment has a successful outcome is 0.8. The experiment is to be repeated until five successful outcomes have occurred. What is the expected number of repetitions required? What is the variance?
Q2. In a 2-week study of the productivity of workers, the following data were obtained on the total number of acceptable pieces:
|
65
|
36
|
49
|
84
|
79
|
56
|
28
|
43
|
67
|
36
|
|
43
|
78
|
37
|
40
|
68
|
72
|
55
|
62
|
22
|
82
|
|
88
|
50
|
60
|
56
|
57
|
46
|
39
|
57
|
73
|
65
|
|
59
|
48
|
76
|
74
|
70
|
51
|
40
|
75
|
56
|
45
|
|
35
|
62
|
52
|
63
|
32
|
80
|
64
|
53
|
74
|
34
|
|
76
|
60
|
48
|
55
|
51
|
54
|
45
|
44
|
35
|
51
|
|
21
|
35
|
61
|
45
|
33
|
61
|
77
|
60
|
85
|
68
|
|
45
|
53
|
34
|
67
|
42
|
69
|
52
|
68
|
52
|
47
|
|
62
|
65
|
55
|
61
|
73
|
50
|
53
|
59
|
41
|
54
|
|
41
|
74
|
82
|
58
|
26
|
35
|
47
|
50
|
38
|
70
|
a. Calculate the sample average
b. Calculate the sample standard deviation
c. Find the median for these data.
d. Construct a stem-and-leaf plot for these data.
e. Construct a histogram for these data.
Q3. The following data represent the yield on 90 consecutive batches of ceramic substrate to which a metal coating has been applied by a vapor-deposition process.
|
94.1
|
87.3
|
94.1
|
92.4
|
84.6
|
85.4
|
93.2
|
84.1
|
94.7
|
|
92.1
|
90.6
|
83.6
|
86.6
|
90.6
|
90.1
|
96.4
|
89.1
|
98.0
|
|
85.4
|
91.7
|
91.4
|
95.2
|
88.2
|
88.8
|
89.7
|
87.5
|
82.6
|
|
88.2
|
86.1
|
86.4
|
86.4
|
87.6
|
84.2
|
86.1
|
94.3
|
84.5
|
|
85.0
|
85.1
|
85.1
|
85.1
|
95.1
|
93.2
|
84.9
|
84.0
|
96.1
|
|
89.6
|
90.5
|
90.0
|
86.7
|
87.3
|
93.7
|
90.0
|
95.6
|
86.4
|
|
92.4
|
83.0
|
89.6
|
87.7
|
90.1
|
88.3
|
87.3
|
95.3
|
89.1
|
|
90.3
|
90.6
|
94.3
|
84.1
|
86.6
|
94.1
|
93.1
|
89.4
|
87.6
|
|
97.3
|
83.7
|
91.2
|
97.8
|
94.6
|
88.6
|
96.8
|
82.9
|
91.1
|
|
86.1
|
93.1
|
96.3
|
84.1
|
94.4
|
87.3
|
90.4
|
86.4
|
83.1
|
a. Compute the mean yield.
b. Compute the standard deviation and the variance of the yield
c. Compute the median yield.
d. Construct a histogram
e. Construct a boxplot for the yield.
Q4. In a lot of 10 components, 2 are sampled at random for inspection. Assume that in fact exactly 2 of the 10 components in the lot are defective. Let X be the number of sampled components that are defective.
a. Find P(X=0).
b. Find P(X=1).
c. Find P(X=2).
d. Find the probability mass function of X.
e. Find the mean of X.
f. Find the standard deviation of X.
Q5. Two different methods are used for predicting the shear strength for steel plate girders. Nine specific girders are randomly selected, and the shear strength measurement is made using each method. The data are shown below:
|
Girder
|
Karlsruch Method
|
Lehigh Method
|
|
1
|
1.186
|
1.061
|
|
2
|
1.151
|
0.992
|
|
3
|
1,322
|
1.063
|
|
4
|
1.339
|
1.062
|
|
5
|
1.200
|
1.065
|
|
6
|
1.402
|
1.178
|
|
7
|
1.365
|
1.037
|
|
8
|
1.537
|
1.068
|
|
9
|
1.559
|
1.052
|
Determine whether there is any difference (on the average) between the two methods.