Stat Homework
Must show work.
Stat
10
4 Chapter 4 Name:________________________
4.2 Homework
page 2
18
#15, 27, 37
15. The values of
x
and y are as follows:
| x |
Y |
|
|
-5 |
10 | |
|
-4 |
18 | |
|
-3 |
||
|
-2 |
26 |
|
|
-1 |
a) Calculate the slope b1 and the y value of the y intercept b0 for the regression line. Write the regression equation.
b) Interpret the values for b1 and b0.
27. Using the data from the previous problem (#15),
a. Predict the value of y for x = -5.
b. Calculate and interpret the prediction error.
c. State whether or not the prediction represents extrapolation.
37. The Chapter 1 Case Study looked at video game sales for the top 30 video games. The following table contains the total sales (y, in game units) and weeks on the top 30 list (x) of 5 randomly chosen video games.
Video game
Total sales
In millions
Of units (y)
Weeks (x)
Super Mario Bros. U for WiiU
1.7
78
NBA 2K14 for PS4
0.6
27
Battlefield 4 for PS3
0.9
29
Titanfall for Xbox One
1.2
10
Yoshi’s New Island for 3DS
0.2
10
a. Calculate the slope, b1, and the y value of the y intercept, b0, of the regression line.
b. State the regression equation in words. (See part c of the solution to example 6 on pages 210-211 for an example of what to say.)
c. Interpret the value for the slope b1 of the regression line, in terms of the variables from the problem. (See part b of the solution for example 7 on page 211 for an example of what to say.)
d. Interpret the value for the y intercept b0 of the regression line, in terms of the variables from the table. (See part a of the solution for example 7 on page 211 for an example of what to say.)
Stat 104 4.2 HW x
Fall 2020 Instructor J Hodgson Page 1 of 2
Stat 104 Chapter 5 Name:________________________
5.1 Homework
page 255 #4-8, 11, 17, 19, 21. 23, page
25
6 #25-29 odd #s, 33, 39, 41, 43, 53, 55, 61, 65, page 257 #73
4. List the three methods for assigning probability.
5. What assumption do we need to make to use the classical method?
6. When can we use the relative frequency method?
7. If we cannot use either the classical method or the relative frequency method, explain how we go about using the subjective method.
8. The experiment is to toss
10
fair coins 25 times each. Which methods can we use to assign probabilities?
11. Is the following a probability model? If not, clearly explain why it is not a probability model.
|
Gender |
Probability |
|
Females |
1.1 |
|
Males |
-0.2 |
Determine the meaning of the following probabilities:
17. The doctor said the chances of recovery from the surgery were near 100%.
19. The stockbroker said the chances were high that the blue chip stock would gain in value this year.
The experiment is to draw a card at random from a shuffled standard deck of 52 cards. Find the following probabilities:
21. Drawing a jack.
23. Drawing the jack of clubs.
The experiment is to roll a fair die once. Find the following probabilities:
25. Observing a 2.
27. Observing a number greater than 2.
29. Observing a 2 or a 3.
33. The experiment is to toss a fair die two times. The outcomes are observing either a number less than 4 or a number greater than or equal to 4. Construct a tree diagram for the experiment.
Consider the experiment of tossing a fair coin twice.
39. Find the probability of observing zero heads.
41. Find the probability of observing two heads.
Consider the experiment of tossing two fair dice and observing the sum of the two dice. Hint: consider the complete sample space perhaps by creating a tree diagram.
43. What is the probability that the sum of the dice equals 9?
53. Suppose that, in a sample of 100 students who drink hot caffeinated beverages, 35 preferred regular coffee,
20
preferred latte, 20 preferred cappuccino, and 25 preferred tea. Find the probability that a randomly selected student prefers cappuccino.
55. Which method of assigning probability did you use to do the previous problem?
61. Use the following frequency table to estimate the probabilities for each color and construct the probability model. A sample of 100 students was asked to name their favorite color.
|
Favorite Color |
Frequency |
||
|
Red |
25 | ||
|
Blue |
|||
|
Green |
20 | ||
|
Black |
10 | ||
|
Violet |
|||
|
Yellow |
65. The Pew Research Internet Project reported that 14 of the 144 people ages 18-29 that it surveyed would someday like to own a time machine.
a. What is the probability that a randomly chosen 18-29 year old would someday like to own a time machine?
b. What is the probability that a randomly chosen 18-29 year old would not someday like to own a time machine?
c. Which method of assigning probability did you use?
73. Consider the experiment of tossing a fair coin three times and observing either heads or tails. Calculate the probability of exactly two heads.
Stat 104 5.1 HW x
Fall 2020 Instructor J Hodgson Page 1 of 2
Stat 104 Chapter 5 Name:________________________
5.2 Homework
page 265 #2, 3, 7, 11, 13, 15, 17, page 266 #19, 21, 23, 25, 27, 33, 35, 39, 41, page 268 #63, page 269 #78
2. Describe the intersection of two mutually exclusive events.
3. Describe the union of two mutually exclusive events.
Consider the experiment of rolling a fair die once. Find the indicated probabilities:
7. Observing a number that is not 6.
11. Ec, where E: {1, 3, 5}
Consider the experiment of drawing a single card at random from a shuffled standard deck of 52 cards. Define the following events. Find the indicated unions and intersections:
J: The card is a jack.
B: The card is a black suit.
S: The card is a spade.
13. J Ⴖ B
15. B Ⴖ S
17. J U S
Find the indicated probabilities for the experiment described in the previous problem:
19. P(J Ⴖ B)
21. P(B Ⴖ S)
23. P(J U S)
The following contingency table contains the counts of those who did and did not survive the sinking of the RMS Titanic, along with whether they were adults or children. Find the following probabilities:
Child
Adult
Total
Did not survive
52
1438
1490
Survived
57
654
711
Total
109
2092
2201
25. P(Child or Adult)
27. P(Child and Survived)
33. P(Adult or Survived)
35. P(Adult or Did not survive)
The following table shows a list of the top 10 largest companies from Forbes magazine’s Global 2000 list. It shows the country and whether the company’s assets surpass $1 trillion.
Company
Country
Assets
Industrial and Commercial Bank of China
China
Over $1 trillion
China Construction Bank
China
Over $1 trillion
Agricultural Bank of China
China
Over $1 trillion
JPMorgan Chase
USA
Over $1 trillion
Berkshire Hathaway
USA
Under $1 trillion
Exxon Mobil`
USA
Under $1 trillion
General Electric
USA
Under $1 trillion
Wells Fargo
USA
Over $1 trillion
Bank of China
China
Over $1 trillion
PetroChina
China
Under $1 trillion
The experiment is to select a company at random. Find the probability of the following:
39. Choosing a company with over $1 trillion in assets.
41. Selecting a company that is from China and has over $1 trillion in assets.
The following table shows the size and recommended gasoline for ten 2014 automobiles.
Car
Car size
Recommended gasoline
BMW 328i
Compact
Premium
Chevrolet Camaro
Compact
Regular
Honda Accord
Compact
Regular
Cadillac CTS
Midsize
Premium
Nissan Sentra
Midsize
Regular
Subaru Legacy AWD
Midsize
Premium
Toyota Camry
Midsize
Regular
Ford Taurus
Large
Regular
Hyundai Genesis
Large
Premium
Rolls-Royce
Large
Premium
Complete the contingency table shown below.
Rec.
Gasoline
Regular
Premium
Total
Car
Compact
Size
Midsize
Large
Total
63. Use the contingency table you filled in to find the following probabilities:
a. Choosing a midsize car that uses premium gasoline.
b. Choosing a midsize car that uses regular gasoline.
c. Selecting a large car that uses premium gasoline.
d. Selecting a large car that uses regular gasoline.
The experiment is to choose one letter at random from a sample of 1000 letters. The sample space is the 26 letters of the alphabet. The total sample size is 1000, so you can find the relative frequencies of the letters in English simply by dividing each frequency by the total sample size.
A
73
B
9
C
30
D
44
E
130
F
28
G
16
H
35
I
74
J
2
K
3
L
35
M
25
N
78
O
74
P
27
Q
3
R
77
S
63
T
93
U
27
V
13
W
16
X
5
Y
19
Z
1
78. Choosing one letter at random, which is it more likely to be, a consonant or a vowel? Show how you made your decision.
Stat 104 5.2 HW x
Fall 2020 Instructor J Hodgson Page 1 of 2
Stat 104 Chapter 5 Name:________________________
5.3A Homework
page 287 #9-21 odd numbers, 33, 53
Contingency table of threatened and endangered species
Africa
Australia
North America
Total
Threatened
1
1
2
4
Endangered
3
1
2
6
Total
4
2
4
10
A mammal is to be chosen at random. Define the following events.
A: Continent is Africa.
B: Continent is Australia.
C: Continent is North America.
E: Mammal is endangered.
T: Mammal is threatened.
Find the indicated probabilities:
9. The mammal is from Africa, given that it is endangered, i.e. P(A given E)
10. P(B given E)
11. P(C given E)
12. P(A given T)
13. P(B given T)
14. P(C given T)
15. The mammal is endangered, given that it is from Africa, i.e. P(E given A).
16. P(E given B)
17. P(E given C)
18. P(T given A)
19. P(T given B)
20. P(T given C)
21. Compare P(E given A) and P(T given A). Among the mammals from Africa, is the higher proportion endangered or threatened?
33. Referring to the work above and using the strategy for determining whether two events are independent, determine whether the following pair of events is independent: species is from Africa, and the species is endangered, i.e. A and E.
53. Use the Multiplication Rule to find the indicated probability:
The National Center for Education Statistics reports that 71% of college students applied for federal financial aid. Of those who applied for federal aid, 47.5% were male. Choosing a student at random what is the probability of selecting a male who applied for federal financial aid?
Stat 104 5.3A HW
Fall 2020 Instructor J Hodgson Page 1 of 2
Stat 104 Chapter 5 Name:________________________
5.3B Homework
page 288 #59, 61, 67, 69, 71, 75, 77, page 289 #79, 85, 93, 100, 101
The National Center for Education Statistics reports the following statistics for surveys of 12,320 female college students and 9,184 male college students:
· 36% of females work 16-25 hours per week
· 38% of males work 16-25 hours per week
A random sample of n=2 college students is taken. Define the following events:
F1: 1st draw is a female who works 16-25 hours per week
F2: 2nd draw is a female who works 16-25 hours per week
M1: 1st draw is a male who works 16-25 hours per week
M2: 2nd draw is a male who works 16-25 hours per week
Use the Multiplication Rule for Independent Events to calculate the indicated probabilities:
59. P(F1 and F2)
61. P(M1 and F2)
Suppose we sample two cards at random and with replacement from a shuffled standard deck of 52 cards. Define the following events:
R1: Red card observed on the first draw.
R2: Red card observed on the second draw.
H1: Heart observed on the first draw.
H2: Heart observed on the second draw.
Find the following probabilities:
67. P(R1 and R2)
69. P(R1 and H2)
Suppose we sample three cards at random and without replacement from a shuffled standard deck of 52 cards. Define the following events:
R1: Red card observed on the first draw.
R2: Red card observed on the second draw.
R3: Red card observed on the third draw.
H1: Heart observed on the first draw.
H2: Heart observed on the second draw.
H3: Heart observed on the third draw.
Find the following probability:
71. P(H1 and R2 and R3)
75. The College Board reports that 48% of the 1.5 million students who took the Natural Sciences subject exam in 2014 had taken 4 years of high school science. If we take a sample of the following number of students, verify that the 1% Guideline applies.
a. n = 2 students
b. n = 3 students
c. n = 5 students
77. Use the 1% Guideline to approximate the probability that n= 3 students who took the Natural Sciences subject exam had taken four years of high school science.
The following contingency table shows the manga (a type of graphic novel) publisher and the weeks on the New York Times Best Seller List for the week of August 24, 2014.
VIZ Media
Kodansha
Seven Seas
Total
1 week
3
1
0
4
2 weeks
3
0
1
4
>2 weeks
0
2
0
2
Total
6
3
1
10
A manga title is to be selected at random. Define the following events:
V: Manga title is published VIZ Media.
K: Manga title is published by Kodansha.
A: Manga title has been on list for one week.
B: Manga title has been on list for two weeks.
C: Manga title has been on list for more than two weeks.
79. Use the alternative method for determining independence to determine whether the following pair of events are independent: V and A.
85. Determine whether the following mutually exclusive events are independent: V and K.
93. Use the Multiplication Rule for n Independent Events to find the probability that E occurs on three successive tosses if E is defined as Observe an even number on a toss of a fair six sided die.
100. Define H: observe a number greater than 3 on a toss of a fair six sided die.
Find the probability that H occurs at least once in ten tosses.
101. Google reports that 50% of incoming emails to Gmail are encrypted. For the random sample of size 2, find the probability that at least one of the emails is encrypted.
Stat 104 5.3B HW
Fall 2020 Instructor J Hodgson Page 1 of 2
Stat 104 Chapter 5
Name:________________________
5.4 Homework
page 303 – 304 #1, 3, 7, 9, 11, 13, 17, 23, 25, 33, 41, 51, 57
1. What type of diagram is helpful in itemizing the possible outcomes of a series of events?
3. What is the difference between a permutation and a combination?
7. A pizza store offers the following options to its customers. Use a tree diagram to list all the possible options from which a customer may choose.
Cheese: no cheese, regular cheese, double cheese.
Pepperoni: no pepperoni, regular pepperoni, double pepperoni.
9. A particular baseball pitcher has to choose from the following options on each pitch. Use a tree diagram to list all the possible options.
Type of pitch: fast ball, curve, slider.
Horizontal position: inside corner, over the plate, outside corner.
Vertical position: High or low.
11. Our 41st president, George Herbert Walker Bush, had four names, with initials GHWB. How many different possible sets of initials are there for people with four names?
13. A college dining service conducted a survey in which it asked students to select their first and second favorite flavors of ice cream from a list of five flavors: vanilla, chocolate, mint chocolate chip, strawberry and maple walnut. How many different possible sets of two favorites are there?
17. Find the value of factorial 6!
23. A woman is considering four sororities to rush this year but only has time to rush two. How many possible orderings are there?
25. Find the value of the permutation nPr = 7P3.
33. Find the value of the combination nCr = 7C3.
41. How many distinct strings of letters can we make by using all the letters in the work PIZZA?
51. A sit-down restaurant has two types of appetizers: garden salad and Buffalo wings. It has three entrees: spaghetti, steak, and chicken. And it offers three kinds of desserts: ice cream, cake, and pie.
a. Draw a tree diagram to find all the different meals a customer can order at this restaurant.
b. How many different meals can a customer order at this restaurant?
57. Five children are playing catch with a ball. How many different ways can one child throw a ball to another child once?
Stat 104 5.4 HW
Fall 2020 Instructor J Hodgson Page 1 of 2
Stat 104 Chapter 6
Name:________________________
6.1 Homework
page 322-324 #5, 9, 17, 23, 25,
27.
29, 30, 31, 39, 45, 49, 53, 57, 63
5. What are the two rules for a discrete probability distribution?
9. Indicate whether the variable is a discrete or continuous random variable: How much coffee will be in your next cup of coffee.
17. Shirelle enjoys listening to album downloads while doing her homework. The probabilities that she will listen to X = 0, 1, 2, 3, or 4 album downloads tonight are 6%, 24%, 38%, 22%, and 10%, respectively.
a. Construct a probability distribution table.
b. Construct a probability distribution graph.
23. For 2014, the College Board reported that 742,000 students had 4 years of high school math, 209,000 had three years of high school math, 30,000 had two years, and 13,000 had one year of high school math when they took their SAT exams.
a. Construct a probability distribution table.
b. Construct a probability distribution graph.
Determine whether the following distributions represent a valid probability distribution. If it does not, explain why not.
25.
X
-10
0
10
P(X)
1/5
1/2
1/5
27.
X
1
2
3
4
5
P(X)
-0.5
0.5
0.7
0.1
0.2
The National Hockey League Championship is decided by a best-of-seven playoff called the Stanley Cup Finals. The following table shows the possible values of X= number of games in the series and the frequency of each value of X, for the Stanley Cup Finals between 1990 and 2014.
X = games
Frequency
4
5
5
5
6
7
7
7
Find the probability that a randomly chosen NHL Championship will have the following number of games:
29. At least six games, X ≥ 6
30. At most six games, X ≤ 6
31. Between 5 and 7 games, inclusive, 5 ≤ X ≤ 7
39. Refer to the probability distribution you calculated in problem #23. Find the probability that a randomly chosen student will have taken either 3 or 4 years of math, i.e. X = 3 or X = 4.
45. For X = the number of album downloads from problem #17:
a. Calculate the mean value of X, µ.
b. Identify the most likely value of X.
c. Find the expected value of X, E(X).
49. For X = the number of games from problems #21, 29-31:
a. Calculate the mean value of X, µ.
b. Identify the most likely value of X.
c. Find the expected value of X, E(X).
53. For X = the number of album downloads from problem #17:
a. Compute the variance of X, ơ2.
b. Calculate the standard deviation of X, ơ.
c. Use the Z score method to determine whether any outliers or unusual data values exist.
57. For X = the number of games from problems #21, 29-31, 49:
a. Compute the variance of X, ơ2.
b. Calculate the standard deviation of X, ơ.
c. Use the Z score method to determine whether any outliers or unusual data values exist.
63. The New York City Police Department tracks the number of vehicles involved in each vehicle collision that occurs in Manhattan. The table shows the frequency distribution for X = the number of vehicles involved in collisions in Manhattan in July 2014.
X = vehicles involved
Frequency
1
288
2
3151
3
109
4
12
5
4
8
1
a. Construct a probability distribution table for X.
b. Find the probability that at least three vehicles are involved in a collision.
c. Find the probability that 6 vehicles are involved in a collision.
d. Find P(1 ≤ X ≤ 3)
e. Calculate P(1 < X < 3).
Stat 104 6.1 HW
Fall 2020 Instructor J Hodgson Page 1 of 2
Stat 104 Chapter 6 Name:________________________
6.2 Homework
page 337-339 #1, 5-13 odd #s, 15, 21, 29, 49, 53, 57, 61
1. State the four requirements for a binomial experiment.
Determine whether the experiment is binomial or not. If the experiment is binomial, identify the random variable X, the number of trials n, the probability of success p, the probability of failure q. If the experiment is not binomial, explain why not.
5. Ask ten of your friends to come to your party (remember the independence assumption).
7. Answer a random sample of eight multiple choice questions either correctly or incorrectly by random guessing. There are four choices, (a) – (d), for each question.
9. Select a student at random in the class until you come across a left-handed student.
11. Four cards are selected at random without replacement from a deck of cards, and the number of queens is observed.
13. Bob has paid to play two games at a carnival. The probability that he wins a particular game is 0.25.
Calculate the probability of X successes for the binomial experiments with the following characteristics:
15. n = 5, p = 0.25, X = 1
21. n = 5, p = 0.25, X ≤ 1
According to the National Center for Education Statistics, business majors accounted for 25% of the proportion of all Master’s degrees granted in 2012. The binomial experiment is to select three Master’s degrees at random and to observe X = number of business majors.
29. Calculate the probability of observing no business majors.
49. For the above situation do the following:
a. Find and interpret the mean µ of X.
b. Calculate the variance ơ2 of X.
c. Compute the standard deviation ơ of X.
53. For the above scenario do the following:
a. Construct the probability distribution graph of X.
b. Identify the mode of X.
57. Suppose that you are taking a quiz of five multiple choice questions (the instructor chose the questions randomly), with each question having four possible responses. You did not study at all for the quiz and will randomly guess which is the correct response for each question. The random variable X is the number of correct responses.
a. If each question has four possible responses, why is this a valid binomial experiment?
b. State the values of n and p.
c. Calculate the probability that you will pass this quiz by correctly responding to at least three of the five questions. Is this good news for you?
d. Use your answer to part (c) to find the probability that you will not pass the quiz.
61. Referring to problem #57:
a. Compute the mean, variance, and standard deviation of X. Interpret the mean.
b. Use the Z score method to determine which numbers of correct response should be considered outliers,
c. Use technology or the binomial table to construct a probability distribution graph of X. Then state the mode of X, that is, the most likely number of correct responses.
Mode:
d. Find the probability that X = the mode.
Stat 104 6.2 HW
Fall 2020 Instructor J Hodgson Page 1 of 2
Stat 104 Chapter 6 Name:___________________________
6.4 Homework
Pg 363-367 #2, 3, 5, 7, 8, 11, 12, 13, 17, 19, 31, 33, 37, 39, 43, 45, 47, 51, 53, 59, 61, 63, 67, 71, 79, 87, 115, 121, 122
2. In the graph of a probability distribution, what is represented on the number line?
3. How is probability represented in the graph of a continuous probability distribution?
5. True or false: The graph of the uniform distribution is always shaped like a square.
7. What is the value for the mean of the standard normal distribution?
8. What is the value for the standard deviation of the standard normal distribution?
Assume that X is a uniform random variable, with left endpoint 0 and right endpoint 100. Find the following probabilities:
11. P(50 < X <100)
12. P(50 ≤ X ≤ 100)
13. P(25 < X < 90)
Assume that X is a uniform random variable, with left endpoint -5 and right endpoint 5. Compute the following probabilities:
17. P(0 ≤ X ≤ 5)
19. P(- 5 ≤ X ≤ – 4)
Birth weights are normally distributed with a mean weight of µ = 3285 grams and a standard deviation of ơ = 500 grams.
31. What is the probability of a birth weight equal to 3285 grams?
33. What is the probability of a birth weight of at least 3285 grams?
Find the area under the standard normal curve that lies to the left of the following:
37. Z = 1
39. Z = 3
43. Z = – 0.2
Find the area under the standard normal curve that lies to the right of the following:
45. Z = 1.27
47. Z = – 3.01
Find the area under the standard normal curve that lies between the following:
51. Z = 2 and Z = 3
53. Z = – 1 and Z = 0
Find the indicated probability for the standard normal Z:
Draw the graph. Find the area using the Z table or technology.
59. P(Z = 0)
61. P(Z < 10)
63. P(Z < - 2.17)
67. P(- 3.05 < Z < - 0.94)
Find the z-value with the following area under the standard normal curve to its left. Draw the graph, and then find the z-value.
71. 0.3336.
Find the z-value with the following area under the standard normal curve to its right. Draw the graph, and then find the z-value.
79. 0.8078
Find the values of z that mark the boundaries of the indicated area:
87. The middle 80%
115. Nicholas took a standardized test and was informed that the z-value of the test score was 1.0. Find the percentages of test takers that Nicholas scored higher than.
121. Find the following areas without using the z table or technology. The area to the left of z = -1.5 is 0.0668.
a. Find the area to the right of z = 1.5.
b. Find the area to the right of z = – 1.5.
c. Find the area between z = – 1.5 and z = 1.5.
122. Find the following areas without using the z table or technology. The area to the right of z = 2.7 is 0.0035.
a. Find the area to the left of z = 2.7.
b. Find the area to the left of z = – 2.7.
c. Find the area between z = – 2.7 and z = 2.7.
Stat 104 6.4 HW Page 1 of 2
Instructor J Hodgson
Stat 104 Chapter 6 Name: __________________________
6.5 HW Page 382 #3, 5, 11, 17, 25, 31
Assume that the random variable X is normally distributed with mean µ = 70 and standard deviation ơ = 10. Draw a graph of the normal curve with the desired probability and value of X indicated. Find the indicated probabilities by standardizing X to Z.
3. P(X>70)
5. P(X<80)
11. P(60≤X≤100)
Using the same random variable X as for the above problems, draw a graph of the normal curve with the desired probability and value of X indicated. Find the indicated values of X using the formula X1 = Zơ + µ.
17. The value of X larger than 97.5% of all X-values.
25. The two symmetric values of X that contain the central 98% of X-values between them.
31. Six-week-old babies consume a mean of µ = 15 ounces of milk per day, with a standard deviation ơ of 2 ounces. Assume that the distribution is normal. Find the probability that a randomly chosen baby consumes the following amounts of milk per day:
a. Less than 15 ounces
b. More than 17 ounces
c. Between 17 and 19 ounces
Stat 104 6.5 HW Page 1 of 2
Fall 2020 Instructor J Hodgson