Spring 2012
Math 227
Final
Name: ______________________
Show your work clearly, neatly, and understandably. Make sure you round the decimal for probability to 5-decimal place and round
the percentage to 3-decimal.
1.
(Total:19)
The mean time taken by all participants to run a road race was found to be 120 minutes with a standard
deviation of 15 minutes. Assume that the times taken for all participants have a normal distribution.
a.
(5) Find
the percentage of runners who finished
c.
(5) Find
d.
(5) A sample
this race in more than 100 min. Draw the
density curve with relevant information.
b.
(4) How
long did it take for the first 70% of
all participants to finish this race?
the probability that a sample of 36
runners have a mean time to finish the race
in at least 130 minutes.
of 7 runners is selected at random.
What is the probability that 3 of them finished
this race in more than 100 min?
2.
3.
Fifteen cards are numbered 1 through 15. The cards are shuffled, and three cards are drawn and
arranged in a row. Find the probability that:
(12: 3,3,6)
a.
(3) All
three cards are even.
b.
(3) The
c.
(6) At
least two cards are less than 10.
first is odd and the last two are even.
(10) A test
of writing ability is given to a random sample of 10 students before and after they completed a
writing course. The results are given below. At 1%-SL, test the claim that the formal writing course
improves students’ writing ability. Assume that the pair of values have differences that are from a
population having a distribution that is approximately normal
After:
Before:
70
69
80
79
92
90
99
96
93
91
97
95
76
75
63
64
68
62
71
64
74
76
4.
5.
(Total 12) Suppose
P(A) = 0.45, P(B) = 0.60, and P(B|A) = 0.30.
d.
a. (3) P(AB)
b.
(2)
P(AB)
c.
(2)
P(A|B)
(5)
P(B|Ac)
(Total 18) A light-bulb
manufacturer advertises that the average life for its energy saving light bulbs is 900
hours. A random sample of 15 of its energy saving light-bulbs resulted in the following lives in hours.
995 590 510 539 739 917 571 555 916 728 664 693 708 887 849
a.
(2)
Compute the best point estimate for the mean of all energy saving light-bulbs.
b.
(4)
Compute the best point estimate for the standard deviation of all energy saving light-bulbs.
c.
(8) Assume
that the population is normally distributed. At 5%-SL, test the claim that the mean life for
the company's light bulbs is less than that from the advertised mean?
d.
(4)
You are hired to estimate the average life for these energy saving light bulbs that are produced by
this company. You want to be 99% confidence that the mean life for such light-bulbs is within 50
hours of the population mean, how many more light bulbs do you need to test?
6.
(Total 35)
The following are the random sample of 40 statistics students.
17
33
39
44
21
33
39
46
25
34
39
47
26
36
41
48
28
36
41
50
30
37
43
52
31
38
43
54
31
38
44
54
31
38
44
55
31
38
44
60
From the data, find:
a.
(2)
Median
a.
(2)
Mode
b.
(2)
Q1
c.
(2)
Q3
d.
(1)
Range
Data are sorted and rounded to the nearest unit for simplicity.
e.
Create a Frequency Distribution with 6 classes and extend to estimate the mean and standard
deviation. Use the smallest data as the starting number
(12:6,2,4)
Interval
Freq
f.
(6)
Create a 95%-CI for the standard deviation.
g.
(8)
Suppose that scoring above 40 is considered passing the Statistics Exam. At 5%-SL, test the claim that
most students are not passing the Statistics Exam. Let p be the population proportion of students not passing
the exam.