Part (I. Short—Answer Questions“ Point-values of questions are as
indicated. spaces ( ) provided after each question. You need not show
'Work and no partial credit will be given, Final answers must be simpliﬁed.
Questions 1, 2 deal with the following freq
Practice Final
Math 231, Spring 2013
Part I
The rst two question are based on the following: For a set of bivariate data (x1 , y1 ), . . . , (x12 , y12 ),
the least squares line is computed to be y = 2 4x. Suppose that the sample mean of x is 1, the
sampl
MATHEMATICS 231
Test 1, Thursday, Oct 4, 2012
Name:
(Please print.)
Please circle your section number and the time your class meets.
Section 010
MWF 9:10a
Section 011
TR 2:35p
This is a closed book exam. You may use a calculator, however, in Part II, you
Homework-015
69. Assume that for a random sample of size 81, the observed sample mean is 6.3, and sample
standard deviation is 2.
a. An interval, (5.9, 6.7), is proposed as a condence interval for the population mean, .
What level of condence is involved?
Mathematics 231 Solution to Problems #68-70, plus S1
X
P (66.4 < X < 75.3)
(68) SOLUTION TO PROBLEM 68: We let
For (a), we are to nd
be the height of a male chosen at random, so,
(since
X
X N (70, 3.12 ).
is a continuous random whose density function has
Homework-014
64. Assume that the lifetime of a certain component has an exponential distribution with mean
3. Find all of the following: the value of the parameter, f , the 55th percentile and the
standard deviation of lifetimes, the probability that a co
Mathematics 231: Probability & Statistics
Assigned Problems
Note: The numbering of exercises refers to the 4th edition of the textbook.
GENERAL DISCLAIMER: All of the statistics given involve completely fictitious,
made-up numbers!
1. A quality control pr
1
MATH 231
Spring, 2014
Assigned Problems- Part II
(Note that the numbering of exercise refers to the 3rd edition of the textbook)
48. A sample of 7 widgets is chosen at random from an enormous lot of widgets in which it is
known that 18% are defective. F
Mathematics 231: Probability & Statistics
Solution for HW02: #10-12
Note: The numbering of exercises refers to the 4th edition of the textbook.
10. An educator wants to see how the number of absences for a student in his class affect
the students final gr
MATHEMATICS 231
Practice Test 1:
Part I. Short-Answer Questions. You need not show work and no partial credit will be given.
Final answers must be simplified.
Question 1-4 all deal with a data set consisting of n = 7 items of bivariate numerical
data (xi
Mathematics 231
Spring 2017
Test 1 Solution
Name:
(Please print.)
Please circle your section:
sec 010: Teboh-Ewungkem
sec 011: Stanley
sec 012: Wu
sec 013: Huang
This is a closed book exam. You may use a calculator, however, in Part I, you must show all
f
Mathematics 231 Solution to Problems #41, 42, 44, 45 plus 50
(41) SOLUTION TO PROBLEM 41: X is a random variable with X = 50 and X = 3. The random variable
Y = 2X + 10.
Y = 2X + 10 = 2 50 + 10 = 90.
2
2
Variance: Y = (2)2 X = 4 9 =
3.
2 =
36 = 6.
Standar
Mathematics 231 Solution to Problems #60-63, plus 65,67
X Poisson(8) ( = 8, since X = 8 = 8 1 and X = ).
0.12408. P (X 4) = 1 P (X 3) = 1 (P (X = 0) + P (X = 1) + P (X =
(60) SOLUTION TO PROBLEM 60: We have that
P (X = 9) =
Thus,
9
e8 8
9!
8
2) + P (X =
Mathematics 231 Solution to Problems #71-72
(71) SOLUTION TO PROBLEM 71: From the assumption that the lifetime, X , (measured in years) of a
randomly selected component has an exponential distribution (with parameter ), we know that X = X =
1
1
, and so,
Mathematics 231: Probability & Statistics
Solution for HW04: #17-22
Note: The numbering of exercises refers to the 4th edition of the textbook.
17. The soccer club has 25 members. In how many ways can it choose a slate of officers for
the four positions:
Mathematics 231: Probability & Statistics
Solution for HW06: #29-34
Note: The numbering of exercises refers to the 4th edition of the textbook.
29. The following table gives the probability mass function of a discrete random variable,
2
X. Determine all o
Mathematics 231: Probability & Statistics
Solution for HW05: #23-28
Note: The numbering of exercises refers to the 4th edition of the textbook.
23. In a certain population, 30.0 % are smokers and 77.0 % of the smokers will develop emphysema. What is the p
MATHEMATICS 231
Practice Test 1:
Part I. Short-Answer Questions. You need not show work and no partial credit will be given.
Final answers must be simplified.
Question 1-4 all deal with a data set consisting of n = 7 items of bivariate numerical
data (xi
Mathematics 231: Probability & Statistics
Solution for HW01
Note: The numbering of exercises refers to the 4th edition of the textbook.
1. A quality control process randomly selects 100 widgets from a production run of 8000
and counts the number of widget
Mathematics 231
Fall 2014
Homework 14 Solution (Problems #87-91,94-96)
87 Let ! be the true (population) mean net weight of cereal in boxes recently packaged at the
mentioned packaging facility. Let X represent the mean weight based on a sample of n
rando
Mathematics 231
Fall 2014
Homework 11 Solution (Problems #71-76)
71 Assume that the lifetime of a certain component has an exponential distribution with mean
5 (and that time is measured in years).
Let X be the lifetime of this component. X !Exp("). Recal
Mathematics 231
Fall 2014
Homework 9 Solution (Problems #54-62)
54 Let X be the random variable representing the number of defective widgets among the 10
randomly chosen widgets. Then X!Bin(10; 0:1) :
! "
10!
a. None of the 10 defective: P (X = 0) = 10
(0
Mathematics 231
Fall 2014
Homework 5 Solution (Problems #29-34)
29 Let S represent the event that a person is a smoker and E the event that a person develops
emphysema. Then P (S) = 0:25 and P (E jS ) = 0:75. Now, by the Law of total probability,
P (E) =
Mathematics 231
Fall 2014
Homework 12 Solution (Problems #77-82)
77 Assume that for a random sample of size 64, with an observed sample mean of 6.4, and
sample standard deviation of 2, the interval (6.05, 6.75) is proposed as a condence interval
for the p
Mathematics 231
Fall 2014
Homework 7 Solution (Problems #41-47 & 50)
41 X is a random variable with !X = 50 and "X = 3. The random variable Y = !2X + 10:
!Y = !2!X + 10 = !2 " 50 + 10 = !90:
2
Variance: "Y2 = (!2)2 "X
= 4 " 9 = 36:
p
p
Standard Deviation:
Mathematics 231
Fall 2014
Homework 6 Solution (Problems #35-40)
35 Question: The following table gives the probability mass function of a discrete random
2
variable, X. Determine all of the following: P (X < 1), P (X ! 0), $X , %X
.
x
-5
0
1
3
p(x) 1/15 4
Mathematics 231
Fall 2014
Homework 10 Solution (Problems #6370)
63 Ten widgets are chosen at random from a lot of 80. If more than three are defective, the lot
is returned for a refund.
Let X be the number of defective widgets in the sample of size 10. Th
Mathematics 231
Homework 15 Solution (Problems #92-93, 97-105)
Fall 2014
92 Do Exercise 16 on p.416.
(iii) 0:01 < P < 0:05. Since the value 4 is inside the 95% condence interval,
P < 0:05. Since it is not inside the 99% condence interval, P > 0:01.
93 Do
MATHEMATICS 231
'Test 2, Thursday, March. 28, 2013
Name: e [1.41" EX ef/ . (Please print.)
Please circle your instructors name and the time your class meets.
Prof. Neel Prof. Stanley Prof.- Wu
TR 1:10 MVVF 9: 10 WT 11:10
This is e'closed book, no notes
Mathematics 231: Probability & Statistics
Solution for HW08: #38-44
Note: The numbering of exercises refers to the 4th edition of the textbook.
38. Refer to Problem ? and answer the following questions. Let Y = X1 + X2 .
(a) Find the mean of Y, Y .
Soluti
Mathematics 231: Probability & Statistics
Solution for HW07: #35-37
Note: The numbering of exercises refers to the 4th edition of the textbook.
35. Two consultants, C1 and C2 are available for assistance on projects. On any given
project, either or both m
Mathematics 231: Probability & Statistics
Solution for HW03: #13-16
Note: The numbering of exercises refers to the 4th edition of the textbook.
13. Do exercise 10 on p. 61 of the textbook. Make sure to explain your answer.
Solution: (Exercise 10 on p. 61.