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Week 3 Assignment: Benchmark - Simulation and Risk Analysis Case Study
The purpose of this assignment is to use analytics techniques to analyze a case problem.Part 1Read Case Study Case 15.2 � ...
Week 3 Assignment: Benchmark - Simulation and Risk Analysis Case Study
The purpose of this assignment is to use analytics techniques to analyze a case problem.Part 1Read Case Study Case 15.2 “Ebony Bath Soap” attached BELOW, and then complete the following items.For Questions 1 and 2 of the case, use the Palisade DecisionTools Excel software to set up a simulation model and run a simulation with 500 trials for the case. Ensure that all Palisade software output is included in your files and that only one Excel file is open when running a simulation. Use the "Topic 3 Case Study Template" file as a starting point. Hint: The RiskSimtable function was be helpful for running the simulations.Respond to Question 3 as written in the problem. Ignore the confidence interval portion of the question.Respond to Question 4 as written in the problem.To receive full credit on the assignment, complete the following.Ensure that the Palisade software output is included with your submission.Ensure that Excel files include the associated cell functions and/or formulas if functions and/or formulas are used.Include a written response to all narrative questions presented in the problem by placing it in the associated Excel file.Include screenshots of all simulation distribution results for output variables.Place each problem in its own Excel file. Ensure that your first and last name are in your Excel file names.Part 2In a 500-750-word summary to company management, address the following. Include relevant charts and graphs within your summary, as needed.Describe the case specific business requirements and how they can be communicated across all levels of the organization.Based on the simulation results, discuss the Annual Cost output statistical distributions. Assume that your audience as minimal background in statistics.Discuss which Annual Cost output probability distribution has the most dispersion, and explain why this is so. Explain the descriptive, predictive, and prescriptive analytics that have been used to formulate the solutions to the business needs.Based on the Annual Cost output statistical distributions and other information gleaned from your analysis, discuss the specific prescribed course of action you would recommend to company management and justify your recommendations. Include discussion of how the proposed analytics solutions can optimize organizational performance and effectiveness.
MATH 524 University of California Operators on Complex Vectors Spaces Questions
this question deals with the “Laguerre Polynomials,” which are orthogonal
with respect to the inner product hf, gi = ...
MATH 524 University of California Operators on Complex Vectors Spaces Questions
this question deals with the “Laguerre Polynomials,” which are orthogonal
with respect to the inner product hf, gi =
Z ∞
0
f(x)g(x) e
−x
dx. Use the fact that
∀ integers p, q ≥ 0 hx
p
, xq
i = (p + q)! (“p plus q factorial”), to derive the first 4 (order
0, 1, 2, 3) orthonormal Laguerre Polynomials starting from elements of the standard
polynomial basis {1, x, x2
, x3}. Let T ∈ L(C
7
) be defined by
T(z1, z2, z3, z4, z5, z6, z7) = (πz1+z2+z3+z4, πz2+z3+z4, πz3+z4, πz4,
√
7z5+z6+z7,
√
7z6+z7,
√
7z7)
Let Bs(C
7
) = {e1, e2, e3, e4, e5, e6, e7} be the standard basis of C
7
(a) (25 pts.) Find M(T, Bs(C
7(b) (25 pts.) Find the eigenvalues {λk}k=1,...,?
(c) For each eigenvalue, λk:
i. (30 pts.) Find the eigenspace E(λk, T)
ii. (30 pts.) Find the generalized eigenspace G(λk, T)
5 pages
20200630031946benchmark Probability And Inferential Statistics 2
1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per decil ...
20200630031946benchmark Probability And Inferential Statistics 2
1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after ...
Elementary Probability and Probability Distributions, statistics homework help
Discussion Random variables are all around you. For example, a random variable could be the number of minutes that you spe ...
Elementary Probability and Probability Distributions, statistics homework help
Discussion Random variables are all around you. For example, a random variable could be the number of minutes that you spend on the phone each day or how many times you check your email each day. For this assignment, you will participate in a discussion about random variables. Instructions 1. Complete the following on the Discussion Board: a. Define the term random variable. b. Post three possible random variables that you encounter in everyday life. An example could be the number of calories you consume each day. Some days you may consume more calories, while other days you may eat less and consume fewer calories. c. Describe each of your examples and explain how they fit the characteristics of being a random variable. 2.1 Assignment Many decisions in life are based upon uncertainty. However, if you know the probability, you may be able to make a more informed decision. For this assignment, you will answer questions and solve problems involving basic probabilities. Instructions 1. Complete the following in a Word document: · Write an original definition of probability based on what you have read. · Write an original definition of sample space based on what you have read. · Write an original definition of event based on what you have read. · Write an original definition of probability distribution based on what you have read. · Write out the sample space for a single toss of a fair coin. · Write out the probability of rolling an odd number if you are rolling a regular six-sided die. · Write out the probability of rolling a number greater than 4 if you are rolling a regular six-sided die. · Write an event where the probability of that event is 0 if you are rolling a regular six-sided die. 2.2 Binomial Distributions For this assignment, you will answer questions and solve problems involving binomial probabilities. Instructions 1. Answer the following questions in a Word document: · Is the binomial distribution a discrete probability distribution or a continuous probability distribution? Explain. · If you are tossing a fair coin 10 times, what is the probability of getting exactly 4 heads out of the 10 coin tosses? · If you are tossing a fair coin 10 times, what is the probability of getting exactly 9 heads out of the 10 coin tosses? · If you are tossing a fair coin 10 times, what is the probability of getting 4 OR 5 heads out of the 10 coin tosses? · The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer hits the target on three shots out of the five. · The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer doesn’t ever hit the target during the five shots. · The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer hits the target on all five shots. 2.3 Probability and Distributions Consider the experiment of tossing a fair coin four times. The coin has two possible outcomes, heads or tails. a. List the sample space for the outcomes that could happen when tossing the coin four times. For example, if all four coin tosses produced heads, then the outcome would be HHHH. b. If each outcome is equally likely, what is the probability that all four coin tosses result in heads? Notice that the complement of “all four heads” is “at least one tail.” Using this information, compute the probability that there will be at least one tail out of the four coin tosses. 1. Suppose you roll a single fair die and note the number rolled. a. What is the sample space for a single roll of a fair die? Are the outcomes equally likely? b. Assign probabilities to the outcomes in the sample space found in part (a). Do these probabilities add up to 1? Should they add up to 1? Why? c. What is the probability of getting a number less than 4 on a single roll? d. What is the probability of getting a 1 or a 2 on a single roll? 3. Suppose we are interested in studying movie ratings where movies get rated on a five star scale. One star means the critic thought the movie was horrible, and five stars means the critic thought it was one of the best movies of the year. Here is a frequency table for all the movies rated by this critic for the year: a. Using this information, if we chose a movie from this group at random, what is the probability that the movie received a: · 1 star rating? · 2 star rating? · 3 star rating? · 4 star rating? · 5 star rating? b. Do the probabilities from part (a) add up to 1? Why should they? What is the sample space in this problem? 4. Given P(A) = 0.6 and P(B) = 0.3 a. If A and B are mutually exclusive events, compute P(A or B). b. If P(A and B) = 0.2, compute P(A or B). c. If A and B are independent events, compute P(A and B). d. If P(B|A) = .1, compute P(A and B). 5. Consider the following events for a college professor selected at random: A = the professor has high blood pressure B = the professor is over 50 years old Translate each of the following scenarios into symbols. For example, the probability a professor has high blood pressure would be P(A). a. The probability a professor has low blood pressure. b. The probability a professor has high blood pressure and is over 50 years old. c. The probability a professor has high blood pressure or is over 50 years old. d. The probability a 40-year-old professor has high blood pressure. e. The probability a professor with high blood pressure is over 50 years old. f. The probability a professor has low blood pressure and is over 50 years old. Rating Number of movies that got that rating 1 Star 28 2 Star 123 3 Star 356 4 Star 289 5 Star 56 6. Suppose we did collect data by asking professors how old they were and measuring their blood pressure. The table below reflects the data collected based on these two variables: Low Blood Pressure High Blood Pressure Total 50 and Under 64 51 115 Over 50 31 73 104 Total 95 124 219 Let us use the following notation for events: U = 50 and under, O = over 50, L = low blood pressure and H = high blood pressure. a. Compute P(L), P(L|U) and P(L|O). b. Are the events L = low blood pressure and U = 50 and under independent? Why or why not? c. Compute P(L and U) and P(L and O). d. Compute P(H) and P(H|U). e. Are the events H = high blood pressure and O = over 50 independent? Why or why not? f. Compute P(L or U). 7. Ryan is a record executive for a hip hop label in Atlanta, Georgia. He has a new album coming out soon, and wants to know the best way to promote it, so he is considering many variables that may have an effect. He is considering three different album covers that may be used, four different television commercials that may be used, and two different album posters that may be used. Determine the number of different combinations he needs in order to test each album cover, television commercial, and album poster. 8. Which of the following are continuous variables, and which are discrete? a. Number of heads out of five coin tosses b. Qualifying speed for the Daytona 500 in miles per hour c. Number of books needed for a literature class d. your weight when you wake up each morning 9. A number of books were reviewed for a history class based on the following scale from 1 to 5: 1=would not recommend the book, 2=cautious or very little recommendation, 3=little or no preference, 4=favorable/recommended book, 5=outstanding/significant contribution. Book Rating, x P(x) 1 .051 2 .099 3 .093 4 .635 5 .122 Suppose a book is selected at random from this group. a. Is this a valid probability distribution? Why? b. Find the probability that the book received a rating of at least 2. How does this probability relate to the probability that book received a rating of 1? c. Find the probability that the book received a rating higher than 3. d. Find the probability that the book received a rating of 3 or higher. e. Compute the average or expected rating of the books in this group. f. Compute the standard deviation for the ratings of the books in this group. 10. Consider a binomial experiment with n = 8 trials where the probability of success on any single trial is p = 0.40. a. Find P(r = 0). b. Find P(r >= 1) using the complement rule. c. Find the probability of getting five successes out of the eight trials. d. Find the probability of getting at least four successes out of the eight trials. 11. Suppose ten people are randomly selected from a population where it is known that 22 percent of the population are smokers. a. For this example, define what a trial would be, what a success would be, and what a failure would be. Also, state the values of n, p and q for this example. b. What is the probability that all ten of the people are smokers? c. What is the probability that none of the ten are smokers? d. What is the probability that at least three of them are smokers? e. What is the probability that no more than two of them are smokers? f. What would be the average or expected amount of smokers out of a sample of ten people from this population?
6.00 Semester 1 Exam (Part 1)
Question 1
Which of the following is an example of a function?
{(-1, 0), (-1, 3), (3, 9), (5, 10)} ...
6.00 Semester 1 Exam (Part 1)
Question 1
Which of the following is an example of a function?
{(-1, 0), (-1, 3), (3, 9), (5, 10)}
{(1, 3), (2, 5), (3, 8), (4, 10)}
{(4, 6), (5, 9), (4, 7)}
{(0, 2), (0, 3), (1, 5), (4, 5)}
2 points
Question 2
What is the inverse of y = 5x + 20? y = 5x + 4 y = 20x - 52 points
Question 3
What is the domain of the following function? {0, 4, 5} {0, 1, 2, 3, 4} {0, 2, 3, 4, 5} {1, 2, 3, 4}2 points
Question 4
Find g º f if f(x) = 2x - 1 and g(x) = x + 2. 2x - 3 2x + 1 2x - 1 2x + 32 points
Question 5
What is the solution of -5x > 25? x > -5 x < -5 x > 5 x < 52 points
Question 6
The solution of is 25. TRUE FALSE2 points
Question 7
The only solution to |r+3|=1 is -2. TRUE FALSE2 points
Question 8
Solve 3|2-x|≥12 x ≤ -2 or x ≥ 6 x ≥ 2 and x ≤ 6 x ≤ -2 x ≥ 62 points
Question 9
Find the slope between points (2, 3) and (-1, 0). -1 1 0 undefined slope2 points
Question 10
What is the slope of the following linear function? -3 3 2 points
Question 11
What is the equation of the following linear function? y = -4x - 4 y = 4x - 4 y = 3x - 4 y = -3x - 42 points
Question 12
What is the equation of a line which includes points (-5, 5) and (2, 5)? x = -5 x = 5 y = 5 y = -52 points
Question 13
The equation of a line with slope m = - and including point (-3, 5) is y = - x - 4. TRUE FALSE2 points
Question 14
The following is the graph of 2x - 8y = 10. TRUE FALSE2 points
Question 15
The following is the graph of y = -x - 6. TRUE FALSE2 points
Question 16
Write the inequality of the following graph. y < -2x - 1 y > 2x - 1 y > -2x - 1 y < 2x - 12 points
Question 17
The following graph is the quadratic parent function. TRUE FALSE2 points
Question 18
What is the a value of the following function? ½ 3 22 points
Question 19
The following is the graph of f(x) = 3(x - 3)2 + 1. TRUE FALSE2 points
Question 20
Which of the following is the equation of g(x) if the parent function is f(x) = x2 and a = 3, h = -5, and k = 6? f(x) = 3(x - 5)2 + 6 f(x) = -3(x + 5)2 + 6 f(x) = 3(x + 5)2 + 6 f(x) = 3(x - 5)2 - 62 points
Question 21
Find the solution to x2 = 36 x = 6 x = -6 x = ±12 x = ±62 points
Question 22
Solve the quadratic equation y2 - 5y = -4 by factoring. {-2, 2} {2, 2} {-1, 4} {4, 1}2 points
Question 23
Solve the quadratic equation x2 - 3x - 10 = 0. {-5, 2} {-2, -5} {-2, 5} {2, 5}2 points
Question 24
Determine the number of solutions of 2x2 - 3x - 5 = 0. 0 1 (double root) 22 points
Question 25
The solution of x2 = 15 + 2x is {3, 5}.TRUEFALSE2 points
Question 26
The solution to x2 + 4x - 1 = 0 is TRUEFALSE2 points
Question 27
Determine the zeros of the function x2 - 16x + 63 = 0. {7, 9} {-7, 9} {-9, 7} {-9, -7}2 points
Question 28
What is the vertex of the function f(x) = x2 - 7x - 18? (- ,- ) (7, -121) ( ,- ) (7, )2 points
Question 29
An
object is launched upward at 64 ft/sec from a platform that is 80 feet
high. What is the objects maximum height if the equation of height (h)
in terms of time (t) of the object is given by h(t) = -16t2 + 64t + 80? 144 feet 123 feet 167 feet 172 feet2 points
Question 30
What is the domain of the following function? x > 2 x < 6 x ≥ 2 and x ≤ 6 All Real Numbers2 points
Question 31
Find the equation of the quadratic function with zeros at -1, and 1 and vertex at (0, -6). y = 6x2 + 6 y = x2 - 1 y = -6x2 - 6 y = 6x2 - 62 points
Question 32
Find the equation of the quadratic function with zeros 10 and 12 and vertex at (11, -2). y = 2x2 - 44x + 120 y = 2x2 - 44x - 240 y = 2x2 - 44x + 240 y = -2x2 - 44x + 2402 points
Question 33
The following is the graph of f(x) = x2 - 9. TRUEFALSE2 points
Question 34
Write the equation for the area (A) in terms of length ( ) of a playground if the width (w) is one half as long as the length ( ). You do not need to solve the equation. A = 2 A = 2 2 2 points
Question 35
Simplify 2 points
Question 36
can be simplified to ¼.TRUEFALSE2 points
Question 37
The following is the graph of the parent function y = . TRUE FALSE2 points
Question 38
The following is the graph of . TRUE FALSE2 points
Question 39
For the parent function y = what effect does the values h = -2 have on the graph? Vertical shift of 2 units down. Vertical shift of 2 units up. Horizontal shift of 2 units to the left. Horizontal shift of 2 units to the right.2 points
Question 40
Given b = 4 and h = 1, what is the equation of the graph if the parent function is y = ? y = y = y = y = 2 points
Question 41
The following is the graph of .
TRUE
FALSE
2 points
Question 42
Find the domain of the function . x ≥ 2 x > 2 x ≥ 4 x < -22 points
Question 43
The solution to the radical function is x = -22. TRUE FALSE2 points
Question 44
Solve . -16, 4 4 -16 -4, 162 points
Question 45
Solve . 6 7 8 92 points
Question 46
Given the following graph, what is the approximate value of the function at x = 4? 1.9 1.8 1.2 12 points
Question 47
Solve . ≤ 4 x ≥ 2 5 ≤ x ≤ 21 x ≤ 5 x ≥ 52 points
Question 48
Does the function y = 8x represent a direct or inverse variation? Direct Variation Inverse Variation2 points
Question 49
If y varies inversely as x. find the constant of variation if y = 6 and x = 2. 3 12 6 42 points
Question 50
Write an appropriate inverse variation equation if y = 11 when x = 3. y = 15x y = 33x 2 points
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Week 3 Assignment: Benchmark - Simulation and Risk Analysis Case Study
The purpose of this assignment is to use analytics techniques to analyze a case problem.Part 1Read Case Study Case 15.2 � ...
Week 3 Assignment: Benchmark - Simulation and Risk Analysis Case Study
The purpose of this assignment is to use analytics techniques to analyze a case problem.Part 1Read Case Study Case 15.2 “Ebony Bath Soap” attached BELOW, and then complete the following items.For Questions 1 and 2 of the case, use the Palisade DecisionTools Excel software to set up a simulation model and run a simulation with 500 trials for the case. Ensure that all Palisade software output is included in your files and that only one Excel file is open when running a simulation. Use the "Topic 3 Case Study Template" file as a starting point. Hint: The RiskSimtable function was be helpful for running the simulations.Respond to Question 3 as written in the problem. Ignore the confidence interval portion of the question.Respond to Question 4 as written in the problem.To receive full credit on the assignment, complete the following.Ensure that the Palisade software output is included with your submission.Ensure that Excel files include the associated cell functions and/or formulas if functions and/or formulas are used.Include a written response to all narrative questions presented in the problem by placing it in the associated Excel file.Include screenshots of all simulation distribution results for output variables.Place each problem in its own Excel file. Ensure that your first and last name are in your Excel file names.Part 2In a 500-750-word summary to company management, address the following. Include relevant charts and graphs within your summary, as needed.Describe the case specific business requirements and how they can be communicated across all levels of the organization.Based on the simulation results, discuss the Annual Cost output statistical distributions. Assume that your audience as minimal background in statistics.Discuss which Annual Cost output probability distribution has the most dispersion, and explain why this is so. Explain the descriptive, predictive, and prescriptive analytics that have been used to formulate the solutions to the business needs.Based on the Annual Cost output statistical distributions and other information gleaned from your analysis, discuss the specific prescribed course of action you would recommend to company management and justify your recommendations. Include discussion of how the proposed analytics solutions can optimize organizational performance and effectiveness.
MATH 524 University of California Operators on Complex Vectors Spaces Questions
this question deals with the “Laguerre Polynomials,” which are orthogonal
with respect to the inner product hf, gi = ...
MATH 524 University of California Operators on Complex Vectors Spaces Questions
this question deals with the “Laguerre Polynomials,” which are orthogonal
with respect to the inner product hf, gi =
Z ∞
0
f(x)g(x) e
−x
dx. Use the fact that
∀ integers p, q ≥ 0 hx
p
, xq
i = (p + q)! (“p plus q factorial”), to derive the first 4 (order
0, 1, 2, 3) orthonormal Laguerre Polynomials starting from elements of the standard
polynomial basis {1, x, x2
, x3}. Let T ∈ L(C
7
) be defined by
T(z1, z2, z3, z4, z5, z6, z7) = (πz1+z2+z3+z4, πz2+z3+z4, πz3+z4, πz4,
√
7z5+z6+z7,
√
7z6+z7,
√
7z7)
Let Bs(C
7
) = {e1, e2, e3, e4, e5, e6, e7} be the standard basis of C
7
(a) (25 pts.) Find M(T, Bs(C
7(b) (25 pts.) Find the eigenvalues {λk}k=1,...,?
(c) For each eigenvalue, λk:
i. (30 pts.) Find the eigenspace E(λk, T)
ii. (30 pts.) Find the generalized eigenspace G(λk, T)
5 pages
20200630031946benchmark Probability And Inferential Statistics 2
1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per decil ...
20200630031946benchmark Probability And Inferential Statistics 2
1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after ...
Elementary Probability and Probability Distributions, statistics homework help
Discussion Random variables are all around you. For example, a random variable could be the number of minutes that you spe ...
Elementary Probability and Probability Distributions, statistics homework help
Discussion Random variables are all around you. For example, a random variable could be the number of minutes that you spend on the phone each day or how many times you check your email each day. For this assignment, you will participate in a discussion about random variables. Instructions 1. Complete the following on the Discussion Board: a. Define the term random variable. b. Post three possible random variables that you encounter in everyday life. An example could be the number of calories you consume each day. Some days you may consume more calories, while other days you may eat less and consume fewer calories. c. Describe each of your examples and explain how they fit the characteristics of being a random variable. 2.1 Assignment Many decisions in life are based upon uncertainty. However, if you know the probability, you may be able to make a more informed decision. For this assignment, you will answer questions and solve problems involving basic probabilities. Instructions 1. Complete the following in a Word document: · Write an original definition of probability based on what you have read. · Write an original definition of sample space based on what you have read. · Write an original definition of event based on what you have read. · Write an original definition of probability distribution based on what you have read. · Write out the sample space for a single toss of a fair coin. · Write out the probability of rolling an odd number if you are rolling a regular six-sided die. · Write out the probability of rolling a number greater than 4 if you are rolling a regular six-sided die. · Write an event where the probability of that event is 0 if you are rolling a regular six-sided die. 2.2 Binomial Distributions For this assignment, you will answer questions and solve problems involving binomial probabilities. Instructions 1. Answer the following questions in a Word document: · Is the binomial distribution a discrete probability distribution or a continuous probability distribution? Explain. · If you are tossing a fair coin 10 times, what is the probability of getting exactly 4 heads out of the 10 coin tosses? · If you are tossing a fair coin 10 times, what is the probability of getting exactly 9 heads out of the 10 coin tosses? · If you are tossing a fair coin 10 times, what is the probability of getting 4 OR 5 heads out of the 10 coin tosses? · The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer hits the target on three shots out of the five. · The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer doesn’t ever hit the target during the five shots. · The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer hits the target on all five shots. 2.3 Probability and Distributions Consider the experiment of tossing a fair coin four times. The coin has two possible outcomes, heads or tails. a. List the sample space for the outcomes that could happen when tossing the coin four times. For example, if all four coin tosses produced heads, then the outcome would be HHHH. b. If each outcome is equally likely, what is the probability that all four coin tosses result in heads? Notice that the complement of “all four heads” is “at least one tail.” Using this information, compute the probability that there will be at least one tail out of the four coin tosses. 1. Suppose you roll a single fair die and note the number rolled. a. What is the sample space for a single roll of a fair die? Are the outcomes equally likely? b. Assign probabilities to the outcomes in the sample space found in part (a). Do these probabilities add up to 1? Should they add up to 1? Why? c. What is the probability of getting a number less than 4 on a single roll? d. What is the probability of getting a 1 or a 2 on a single roll? 3. Suppose we are interested in studying movie ratings where movies get rated on a five star scale. One star means the critic thought the movie was horrible, and five stars means the critic thought it was one of the best movies of the year. Here is a frequency table for all the movies rated by this critic for the year: a. Using this information, if we chose a movie from this group at random, what is the probability that the movie received a: · 1 star rating? · 2 star rating? · 3 star rating? · 4 star rating? · 5 star rating? b. Do the probabilities from part (a) add up to 1? Why should they? What is the sample space in this problem? 4. Given P(A) = 0.6 and P(B) = 0.3 a. If A and B are mutually exclusive events, compute P(A or B). b. If P(A and B) = 0.2, compute P(A or B). c. If A and B are independent events, compute P(A and B). d. If P(B|A) = .1, compute P(A and B). 5. Consider the following events for a college professor selected at random: A = the professor has high blood pressure B = the professor is over 50 years old Translate each of the following scenarios into symbols. For example, the probability a professor has high blood pressure would be P(A). a. The probability a professor has low blood pressure. b. The probability a professor has high blood pressure and is over 50 years old. c. The probability a professor has high blood pressure or is over 50 years old. d. The probability a 40-year-old professor has high blood pressure. e. The probability a professor with high blood pressure is over 50 years old. f. The probability a professor has low blood pressure and is over 50 years old. Rating Number of movies that got that rating 1 Star 28 2 Star 123 3 Star 356 4 Star 289 5 Star 56 6. Suppose we did collect data by asking professors how old they were and measuring their blood pressure. The table below reflects the data collected based on these two variables: Low Blood Pressure High Blood Pressure Total 50 and Under 64 51 115 Over 50 31 73 104 Total 95 124 219 Let us use the following notation for events: U = 50 and under, O = over 50, L = low blood pressure and H = high blood pressure. a. Compute P(L), P(L|U) and P(L|O). b. Are the events L = low blood pressure and U = 50 and under independent? Why or why not? c. Compute P(L and U) and P(L and O). d. Compute P(H) and P(H|U). e. Are the events H = high blood pressure and O = over 50 independent? Why or why not? f. Compute P(L or U). 7. Ryan is a record executive for a hip hop label in Atlanta, Georgia. He has a new album coming out soon, and wants to know the best way to promote it, so he is considering many variables that may have an effect. He is considering three different album covers that may be used, four different television commercials that may be used, and two different album posters that may be used. Determine the number of different combinations he needs in order to test each album cover, television commercial, and album poster. 8. Which of the following are continuous variables, and which are discrete? a. Number of heads out of five coin tosses b. Qualifying speed for the Daytona 500 in miles per hour c. Number of books needed for a literature class d. your weight when you wake up each morning 9. A number of books were reviewed for a history class based on the following scale from 1 to 5: 1=would not recommend the book, 2=cautious or very little recommendation, 3=little or no preference, 4=favorable/recommended book, 5=outstanding/significant contribution. Book Rating, x P(x) 1 .051 2 .099 3 .093 4 .635 5 .122 Suppose a book is selected at random from this group. a. Is this a valid probability distribution? Why? b. Find the probability that the book received a rating of at least 2. How does this probability relate to the probability that book received a rating of 1? c. Find the probability that the book received a rating higher than 3. d. Find the probability that the book received a rating of 3 or higher. e. Compute the average or expected rating of the books in this group. f. Compute the standard deviation for the ratings of the books in this group. 10. Consider a binomial experiment with n = 8 trials where the probability of success on any single trial is p = 0.40. a. Find P(r = 0). b. Find P(r >= 1) using the complement rule. c. Find the probability of getting five successes out of the eight trials. d. Find the probability of getting at least four successes out of the eight trials. 11. Suppose ten people are randomly selected from a population where it is known that 22 percent of the population are smokers. a. For this example, define what a trial would be, what a success would be, and what a failure would be. Also, state the values of n, p and q for this example. b. What is the probability that all ten of the people are smokers? c. What is the probability that none of the ten are smokers? d. What is the probability that at least three of them are smokers? e. What is the probability that no more than two of them are smokers? f. What would be the average or expected amount of smokers out of a sample of ten people from this population?
6.00 Semester 1 Exam (Part 1)
Question 1
Which of the following is an example of a function?
{(-1, 0), (-1, 3), (3, 9), (5, 10)} ...
6.00 Semester 1 Exam (Part 1)
Question 1
Which of the following is an example of a function?
{(-1, 0), (-1, 3), (3, 9), (5, 10)}
{(1, 3), (2, 5), (3, 8), (4, 10)}
{(4, 6), (5, 9), (4, 7)}
{(0, 2), (0, 3), (1, 5), (4, 5)}
2 points
Question 2
What is the inverse of y = 5x + 20? y = 5x + 4 y = 20x - 52 points
Question 3
What is the domain of the following function? {0, 4, 5} {0, 1, 2, 3, 4} {0, 2, 3, 4, 5} {1, 2, 3, 4}2 points
Question 4
Find g º f if f(x) = 2x - 1 and g(x) = x + 2. 2x - 3 2x + 1 2x - 1 2x + 32 points
Question 5
What is the solution of -5x > 25? x > -5 x < -5 x > 5 x < 52 points
Question 6
The solution of is 25. TRUE FALSE2 points
Question 7
The only solution to |r+3|=1 is -2. TRUE FALSE2 points
Question 8
Solve 3|2-x|≥12 x ≤ -2 or x ≥ 6 x ≥ 2 and x ≤ 6 x ≤ -2 x ≥ 62 points
Question 9
Find the slope between points (2, 3) and (-1, 0). -1 1 0 undefined slope2 points
Question 10
What is the slope of the following linear function? -3 3 2 points
Question 11
What is the equation of the following linear function? y = -4x - 4 y = 4x - 4 y = 3x - 4 y = -3x - 42 points
Question 12
What is the equation of a line which includes points (-5, 5) and (2, 5)? x = -5 x = 5 y = 5 y = -52 points
Question 13
The equation of a line with slope m = - and including point (-3, 5) is y = - x - 4. TRUE FALSE2 points
Question 14
The following is the graph of 2x - 8y = 10. TRUE FALSE2 points
Question 15
The following is the graph of y = -x - 6. TRUE FALSE2 points
Question 16
Write the inequality of the following graph. y < -2x - 1 y > 2x - 1 y > -2x - 1 y < 2x - 12 points
Question 17
The following graph is the quadratic parent function. TRUE FALSE2 points
Question 18
What is the a value of the following function? ½ 3 22 points
Question 19
The following is the graph of f(x) = 3(x - 3)2 + 1. TRUE FALSE2 points
Question 20
Which of the following is the equation of g(x) if the parent function is f(x) = x2 and a = 3, h = -5, and k = 6? f(x) = 3(x - 5)2 + 6 f(x) = -3(x + 5)2 + 6 f(x) = 3(x + 5)2 + 6 f(x) = 3(x - 5)2 - 62 points
Question 21
Find the solution to x2 = 36 x = 6 x = -6 x = ±12 x = ±62 points
Question 22
Solve the quadratic equation y2 - 5y = -4 by factoring. {-2, 2} {2, 2} {-1, 4} {4, 1}2 points
Question 23
Solve the quadratic equation x2 - 3x - 10 = 0. {-5, 2} {-2, -5} {-2, 5} {2, 5}2 points
Question 24
Determine the number of solutions of 2x2 - 3x - 5 = 0. 0 1 (double root) 22 points
Question 25
The solution of x2 = 15 + 2x is {3, 5}.TRUEFALSE2 points
Question 26
The solution to x2 + 4x - 1 = 0 is TRUEFALSE2 points
Question 27
Determine the zeros of the function x2 - 16x + 63 = 0. {7, 9} {-7, 9} {-9, 7} {-9, -7}2 points
Question 28
What is the vertex of the function f(x) = x2 - 7x - 18? (- ,- ) (7, -121) ( ,- ) (7, )2 points
Question 29
An
object is launched upward at 64 ft/sec from a platform that is 80 feet
high. What is the objects maximum height if the equation of height (h)
in terms of time (t) of the object is given by h(t) = -16t2 + 64t + 80? 144 feet 123 feet 167 feet 172 feet2 points
Question 30
What is the domain of the following function? x > 2 x < 6 x ≥ 2 and x ≤ 6 All Real Numbers2 points
Question 31
Find the equation of the quadratic function with zeros at -1, and 1 and vertex at (0, -6). y = 6x2 + 6 y = x2 - 1 y = -6x2 - 6 y = 6x2 - 62 points
Question 32
Find the equation of the quadratic function with zeros 10 and 12 and vertex at (11, -2). y = 2x2 - 44x + 120 y = 2x2 - 44x - 240 y = 2x2 - 44x + 240 y = -2x2 - 44x + 2402 points
Question 33
The following is the graph of f(x) = x2 - 9. TRUEFALSE2 points
Question 34
Write the equation for the area (A) in terms of length ( ) of a playground if the width (w) is one half as long as the length ( ). You do not need to solve the equation. A = 2 A = 2 2 2 points
Question 35
Simplify 2 points
Question 36
can be simplified to ¼.TRUEFALSE2 points
Question 37
The following is the graph of the parent function y = . TRUE FALSE2 points
Question 38
The following is the graph of . TRUE FALSE2 points
Question 39
For the parent function y = what effect does the values h = -2 have on the graph? Vertical shift of 2 units down. Vertical shift of 2 units up. Horizontal shift of 2 units to the left. Horizontal shift of 2 units to the right.2 points
Question 40
Given b = 4 and h = 1, what is the equation of the graph if the parent function is y = ? y = y = y = y = 2 points
Question 41
The following is the graph of .
TRUE
FALSE
2 points
Question 42
Find the domain of the function . x ≥ 2 x > 2 x ≥ 4 x < -22 points
Question 43
The solution to the radical function is x = -22. TRUE FALSE2 points
Question 44
Solve . -16, 4 4 -16 -4, 162 points
Question 45
Solve . 6 7 8 92 points
Question 46
Given the following graph, what is the approximate value of the function at x = 4? 1.9 1.8 1.2 12 points
Question 47
Solve . ≤ 4 x ≥ 2 5 ≤ x ≤ 21 x ≤ 5 x ≥ 52 points
Question 48
Does the function y = 8x represent a direct or inverse variation? Direct Variation Inverse Variation2 points
Question 49
If y varies inversely as x. find the constant of variation if y = 6 and x = 2. 3 12 6 42 points
Question 50
Write an appropriate inverse variation equation if y = 11 when x = 3. y = 15x y = 33x 2 points
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