Probability and Statistics
FTU
Midterm examination
Time: 60 minutes
No note is allowed
Instruction: Show all steps of your work to receive full credit. Take 2 decimal places for your results.
1) (2 pts) The following probability distributions of satisfaction scores for a sample of information
technology students range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).
Satisfaction scores
1
2
3
4
5
Students
0.05
0.08
0.4
0.35
0.12
What is the weighted mean of the satisfaction score for students?
2) (1 pt) Draw the steam-and-leaf for the data
33, 35, 47, 49, 53, 59, 61, 38, 43, 65, 73, 78, 80
3) (2 pts) Determine the 35th and the 85th percentiles in the following data
69
91
62
103
66
109
73
116
75
122
79
127
80
130
79
94
59
79
51
63
83
135
88
138
95
152
4) (2 pts) Consider the following data:
65
70
98
62
55
66
62
80
90
73
72
71
56
85
a) How many classes would you recommend ?
b) What class interval would you suggest ?
c) What lower limit would you recommend for the first class ?
d) Construct a frequency distribution
March 5, 2022
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Probability and Statistics
FTU
5) (2 pts) A recent survey reported in BusinessWeek dealt with the salaries of CEOs at large corporations and whether company shareholders made money or lost money.
Shareholders made money
Shareholders lost money
Total
CEO Paid More Than $1 Million
2
4
6
CEO Paid Less Than $1 Million
11
3
14
Total
13
7
20
If a company is randomly selected from the list of 20 studied, what is the probability:
(a)
(b)
(c)
(d)
The
The
The
The
CEO made more than $1 million ?
CEO made more than $1 million or the shareholders lost money ?
CEO made more than $1 million if we know the shareholders lost money ?
shareholders lost money if we know the CEO made less than $1 million ?
6) (1 pt) A fair coin is continually flipped. What is the probability that the first 4 flips are:
(a) H,H,H,H
(b) T,H,H,H
(c) What is the probability that the pattern T,H,H,H occurs before the pattern H,H,H,H ?
THE END
March 5, 2022
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