Statistics 200 - Hmwrk
STATS 200 - WEEK 3 Homework
1. Exercise #7, Pg 216, Lane Chp 5
Answer: a) 1/8
b) 7/8
3. Exercise #27, Pg 221, Lane Chp 5
A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos.
Answer: b) 15/484 = .031
c) 149/968 = 0.154
4. Exercise #86, Pg 207, Illowsky Chp 3
Roll two fair dice. Each die has six faces.
a. List the sample space.
Answer:
b. LetAbe the event that either a three or four is rolled first, followed by an even number. FindP(A).
Answer:
c. LetBbe the event that the sum of the two rolls is at most seven. FindP(B).
Answer:
d. In words, explain what “P(A|B)” represents. FindP(A|B).
Answer:
e. AreAandBmutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.
Answer:
f. AreAandBindependent events? Explain your answer in one to three complete sentences, including numerical justification.
Answer:
5. Exercise #98, Pg 209, Illowsky Chp 3
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. LetFbe the event that a course has a final exam. LetRbe the event that a course requires a research paper.
a.Find the probability that a course has a final exam or a research project.
Answer:
b.Find the probability that a course has NEITHER of these two requirements.
Answer:
6. Exercise #112, Pg 210, Illowsky Chp 3
Table Below identifies a group of children by one of four hair colors, and by type of hair.
|
Hair Type |
Brown |
Blond |
Black |
Red |
Totals |
|
Wavy |
20 |
|
15 |
3 |
43 |
|
Straight |
80 |
15 |
|
12 |
|
|
Totals |
|
20 |
|
|
215 |
a.Complete the table above.
b.What is the probability that a randomly selected child will have wavy hair?
Answer:
c.What is the probability that a randomly selected child will have either brown or blond hair?
Answer:
d.What is the probability that a randomly selected child will have wavy brown hair?
Answer:
e.What is the probability that a randomly selected child will have red hair, given that he or she has
straight hair?
Answer:
f.IfBis the event of a child having brown hair, find the probability of the complement ofB.
Answer:
g. In words, what does the complement ofBrepresent?
Answer:
7. Exercise #124, Pg 214, Illowsky Chp 3
The percent of licensed U.S. drivers (from a recent year) that are female is 48.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Of the licensed U.S. male drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.
Suppose that 10,000 U.S. licensed drivers are randomly selected.
a.How many would you expect to be male?
Answer:
b.Using the table or tree diagram, construct a contingency table of gender versus age group.
Answer:
c.Using the contingency table, find the probability that out of the age 20–64 group, a randomly selected driver is female.
Answer:
8. Exercise #72, Pg 268, Illowsky Chp 4
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.
Answer:
9. Exercise #80, Pg 270, Illowsky Chp 4
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?
Answer:
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 variableXequal the size of the student’s class. Define the PDF forX.
Answer:
10. Exercise #88, Pg 271, Illowsky Chp 4
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 variableX.
Answer:
b.List the values thatXmay take on.
Answer:
c.Give the distribution ofX.X ~ _____(_____,_____)
Answer:
d.How many of the 12 students do we expect to attend the festivities?
Answer:
e.Find the probability that at most four students will attend.
Answer:
f.Find the probability that more than two students will attend.
Answer:
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Solution: Statistics 200 - Hmwrk