Mathematics
Lane Questions http://onlinestatbook.com/Online_Statistics_Education.pdf
Chapter 5, Exercise 5, Page 216
5. A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?
Chapter 5, Exercise 7, Page 216
7.You flip a coin three times. (a) What is the probability of getting heads on only
one of your flips? (b) What is the probability of getting heads on at least one flip?
Chapter 5, Exercise 9, Page 217
9. A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement). (a) What is the probability that one will be green and the other red? (b) What is the probability that one will be blue and the other yellow?
Chapter 5, Exercise 27, Page 221
27. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos.
a. Imagine you stick your hand in this refrigerator and pull out a piece of fruit at random. What is the probability that you will pull out a pear?
b. Imagine now that you put your hand in the refrigerator and pull out a piece of fruit. You decide you do not want to eat that fruit so you put it back into the refrigerator and pull out another piece of fruit. What is the probability that the first piece of fruit you pull out is a banana and the second piece you pull out is an apple?
c. What is the probability that you stick your hand in the refrigerator one time and pull out a mango or an orange?
Illowsky Questions https://d3bxy9euw4e147.cloudfront.net/oscms-prodcms/media/documents/Introductory_Statistics-OP.pdf
Chapter 3, Exercise 86, Page 210
86. Roll two fair dice. Each die has six faces.
a. List the sample space.
b. Let A be the event that either a three or four is rolled first, followed by an even number. Find P(A).
c. Let B be the event that the sum of the two rolls is at most seven. Find P(B).
d. In words, explain what “P(A|B)” represents. Find P(A|B).
e. Are A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.
f. Are A and B independent events? Explain your answer in one to three complete sentences, including numerical justification.
Chapter 3, Exercise 98, Page 212
98. At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the event that a course has a final exam. Let R be the event that a course requires a research paper.
a. Find the probability that a course has a final exam or a research project.
b. Find the probability that a course has NEITHER of these two requirements.
Chapter 3, Exercise 112, Page 213
112. Table 3.22 identifies a group of children by one of four hair colors, and by type of hair.
Hair Type | Brown | Blonde | Black | Red | Totals |
Wavy | 20 | 15 | 3 | 43 | |
Straight | 80 | 15 | 12 | ||
Totals | 20 | 215 |
a. Complete the table.
b. What is the probability that a randomly selected child will have wavy hair?
c. What is the probability that a randomly selected child will have either brown or blond hair?
d. What is the probability that a randomly selected child will have wavy brown hair?
e. What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?
f. If B is the event of a child having brown hair, find the probability of the complement of B.
g. In words, what does the complement of B represent?
Chapter 4, Exercise 72, Page 271
72. You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes. Find your expected gain or loss.
Chapter 4, Exercise 80, Page 273
80. Florida State University has 14 statistics classes scheduled for its Summer 2013 term. One class has space available for 30 students, eight classes have space for 60 students, one class has space for 70 students, and four classes have space for
100 students.
a. What is the average class size assuming each class is filled to capacity?
b. Space is available for 980 students. Suppose that each class is filled to capacity and select a statistics student at random. Let the random variable X equal the size of the student’s class. Define the PDF for X.
Chapter 4, Exercise 88, Page 274
88. A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. How many of the 12 students do we expect to attend the festivities?
e. Find the probability that at most four students will attend.
f. Find the probability that more than two students will attend.
Quiz
(For Questions 1, 2, & 3) There are 31 participants in a special high-adventure camp at Goshen Scout Camp last September. Following is a list of the age of the participants.
16, 18, 13, 24, 17, 17, 18, 14, 14, 16, 14, 20, 22, 21, 15
11, 13, 26, 27, 13, 16, 17, 17, 14, 19, 15, 17, 16, 19, 19, 28
1. (7 points) Prepare a frequency distribution of the participants’ ages with a class width of 2 years, and another with class width of 5 years.
2. (6 points) Construct a histogram of the participants’ age with a class width of 2 years and another with a class width of 5 years. What can we say about the choice of class width?
3. (5 points) Give a 5-number summary of the ages of the participants, and construct the corresponding boxplot.
(For Questions 4 & 5) Below please find a hypothetical (imaginary) data set for the enrollment number in our three statistics classes over the past few years. Please note that STAT 225 was not in existence until the fall of 2006.
STAT 200 | STAT 225 | STAT 230 | |
Spring 2006 | 335 | —– | 388 |
Summer 2006 | 191 | —– | 178 |
Fall 2006 | 404 | 141 | 445 |
Spring 2007 | 406 | 154 | 463 |
Summer 2007 | 225 | 43 | 218 |
Fall 2007 | 308 | 129 | 352 |
Spring 2008 | 320 | 81 | 314 |
Summer 2008 | 196 | 42 | 156 |
Fall 2008 | 324 | 80 | 347 |
Spring 2009 | 375 | 92 | 332 |
Summer 2009 | 233 | 50 | 204 |
Fall 2009 | 406 | 112 | 334 |
Spring 2010 | 432 | 114 | 336 |
Summer 2010 | 230 | 49 | 203 |
Fall 2010 | 414 | 121 | 317 |
Spring 2011 | 498 | 119 | 318 |
Summer 2011 | 250 | 55 | 174 |
Fall 2011 | 544 | 140 | 196 |
Spring 2012 | 554 | 166 | 365 |
Summer 2012 | 317 | 82 | 185 |
Fall 2012 | 546 | 168 | 372 |
Spring 2013 | 643 | 134 | 312 |
4. (9 points) There are many graphical format to illustrate a given data set. However, some formats are better than others in the sense that they convey important and relevant information in the given data set. For the given data set, pick the most appropriate graphic format to present the above data set, and plot the given data. Feel free to process the data set and/or include additional information you can deduce from the data set that you think can be useful make your point.
5. (7 points) At times, there may be unwarranted features in the plots you come up with, even though they are true representation of the given data. We may call that data noise, and it will distract us from conveying essential information in the data set. Do you encounter this situation in your plot? If so, what would you do to minimize distractions without misrepresenting the data?
(For Questions 6, 7, & 8) I have a collection of 5 ancient gold coins. Their weights, in ounces, are 23.1, 18.6, 33.5, 12.4, and 27.1.
6. (2 points) What is the mean weight of my ancient gold coins?
7. (2 points) How do you consider this collection, a population or a sample? Why?
8. (2 points) What is the variance and standard deviation in weight of my coin collection?
Discussion Question
Let me tell you a little dirty secret about the mutual dislike between mathematicians and physicists. It can escalate into a full-blown war if diplomacy is not attempted properly.
It happens that a graduate student in theoretical/mathematical physics is looking for five members of his dissertation committee. He has been working closely with three professors in the mathematics department, and 5 professors in the physics department on his dissertation research.
Now comes the monkey wrench.
The mathematics department demands that the chair of the dissertation committee must be a mathematician in order to keep the physicists in check. What? How arrogant! But, there is no other choice if a dissertation committee has to be assembled in time. As usual, physicists have to swallow their pride in order to keep peace. Yes, they are just a bunch of you know what (click on the link ) in the mathematics department!
Question: For comic relief, can you figure out how may ways can this helpless graduate student can choose among his beloved professors if the chair of the committee must be a mathematician, and the rest of the committee can be a mix of mathematicians and physicists?
Well, wouldn’t this be great?
OK, let’s get serious……. Can you help our helpless graduate student?
And let’s be more charitable to mathematicians………., if you can……….