Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

4.16 Given the probability distribution function:x 0 1 2 Probability 0.25 0.50 0.25a. Graph the probability distribution function.b. Calculate and graph the cumulative probability distribution.c. Find the mean of the random variable X.d. Find the variance of X.
4.15 Consider the probability distribution function.x 0 1 Probability 0.30 0.70a. Graph the probability distribution function.b. Calculate and graph the cumulative probability distribution.c. Find the mean of the random variable X.d. Find the variance of X.
4.13 The number of computers sold per day at Dan’s Computer Works is defined by the following probability distribution:x 0 1 2 3 4 5 6 P(x) 0.03 0.11 0.15 0.22 0.19 0.26 0.04a. P(3 … x 6 6) = ?b. P(x 7 3) = ?c. P(x … 4) = ?d. P(2 6 x … 5) = ?
4.11 Show the probability distribution function of the number of heads when three fair coins are tossed independently.
4.10 Show the probability distribution function of the face values of a single die when a fair die is rolled.
4.6 List three continuous random variables that a portfolio manager at an investment firm should regularly examine.
4.5 List four examples of discrete random variables that could be observed in education.
4.7 Jointly Distributed Discrete Random Variables Conditional Mean and Variance Computer Applications Linear Functions of Random Variables Covariance Correlation Portfolio Analysis
4.6 Hypergeometric Distribution
4.5 Poisson Distribution Poisson Approximation to the Binomial Distribution Comparison of the Poisson and Binomial Probability Distributions
4.4 Binomial Distribution Developing the Binomial Distribution
4.3 Properties of Discrete Random Variables Expected Value of a Discrete Random Variable Variance of a Discrete Random Variable Mean and Variance of Linear Functions of a Random Variable
4.2 Probability Distributions for Discrete Random Variables
4.1 Random Variables
3.113 A furniture manufacturer in Sweden indicates that 55% of the tables and 30% of the chairs produced are supplied to retailer A. Of the total units produced, 65% are chairs and the remainder are tables.a. What is the probability that a randomly chosen unit is a chair and will be supplied to
3.112 The accompanying table shows, for 1,000 forecasts of earnings per share made by financial analysts, the numbers of forecasts and outcomes in particular categories(compared with the previous year).Forecast Outcome Improvement About the Same Worse Improvement 210 82 66 About the same 106 153 75
3.108 An economist is analyzing the amount of gasoline (in millions of liters) a producer is willing to supply at each price level (in € per gallon). Long-term analysis indicates that 90% of the gasoline producers are willing to increase supply when there is an increase of€0.20 per liter in the
3.104 An 8-page document contains one page with typographical errors. Two pages are chosen randomly from the document.a. How many different combinations of two pages could be chosen?b. What is the probability that the page with the errors will be chosen?
3.103 A manager at a toy store makes a random selection of 10 balls from a box containing 7 yellow balls and 6 green balls.a. How many different selections are possible?b. What is the probability that a majority of the yellow balls will be selected?
3.97 Suppose a student needs to apply for a loan to enroll at the University of Melbourne, Australia. She believes that there is a 0.8 probability that the loan will be approved within the next three months if the bank interest rate remains the same, and a 0.4 probability that the loan will be
3.95 Show that the probability of an event A can be written as follows:P1A2 = P1A < B2 - P1B231 - P1AuB24
3.93 What is the relationship between the joint probability, marginal probability, and conditional probability?Provide an example to illustrate the relationship.
3.92 State with evidence, whether each of the following statements is true or false:a. If two events are mutually exclusive, the probability of their union is the sum of their probabilities.b. The sum of the probabilities of two events cannot be more than 2.c. The sum of the probabilities of an
3.90 What is conditional probability? Explain using a suitable real-life example.
3.88 After attending a statistics lecture on probability, your classmate is unclear on the difference between mutually exclusive events and independent events. Explain the differences between the two types of events with suitable examples.
3.82 Given P1B12 = 0.65, P1A2 uB12 = 0.15, and P1A2 uB22 = 0.45, what is the probability of P1B2 uA22?
3.81 Given P1B12 = 0.15, P1A2 uB12 = 0.60, and P1A2 uB22 = 0.30, what is the probability of P1B1 uA12?
3.80 Given P1A12 = 0.32, P1B1 uA12 = 0.70, and P1B1 uA22 = 0.51, what is the probability of P1A2 uB12?
3.79 Given P1A12 = 0.80, P1B1 uA12 = 0.55, and P1B1 uA22 = 0.20, what is the probability of P1A1 uB22?
3.78 Given P1A12 = 0.38, P1B1 uA12 = 0.87, and P1B1 uA22 = 0.42, what is the probability of P1A1 uB12?
3.75 Before books aimed at preschool children are marketed, reactions are obtained from a panel of preschool children. These reactions are categorized as favorable, neutral, or unfavorable. Subsequently, book sales are categorized as high, moderate, or low, according to the norms of this market.
3.70 The accompanying table shows proportions of adults in metropolitan areas, categorized as to whether they are public-radio contributors and whether or not they voted in the last election.Voted Contributors Noncontributors Yes 0.63 0.13 No 0.14 0.10a. What is the probability that a randomly
3.69 The accompanying table shows proportions of computer salespeople classified according to marital status and whether they left their jobs or stayed over a period of 1 year.Time on job Marital Status Úone year 6 one year Married 0.64 0.13 Single 0.17 0.06a. What is the probability that a
3.68 A form was circulated among the employees at the Sinopec Group, one of the world’s largest oil refining, gas and petrochemical conglomerate, asking them if they are planning to apply for leaves in August(Yes/No) and their preferred location. The following table gives proportions of employees
3.66 Subscribers to a local newspaper were asked whether they regularly, occasionally, or never read the business section and also whether they had traded common stocks (or shares in a mutual fund) over the last year. The table shown here indicates the proportions of subscribers in six joint
3.65 An analyst at an airline company wants to predict whether the number of passengers for the various cabin classes will decrease, remain the same, or increase over the next year. The following table shows predictions based on the past records.Prediction Decrease Remains the same Increase Economy
3.64 A survey carried out for a supermarket classified customers according to whether their visits to the store are frequent or infrequent and whether they often, sometimes, or never purchase generic products. The accompanying table gives the proportions of people surveyed in each of the six joint
3.60 The probability of a sale is 0.50. What are the odds in favor of a sale?
3.59 The probability of a sale is 0.80. What are the odds in favor of a sale?
3.58 What is the conditional probability that a Masters student prefers Documentaries?
3.57 What is the conditional probability a student who prefers Movies/Series is a Bachelors student?
3.56 What is the conditional probability that a student who prefers watching News is a Bachelors student?
3.55 What is the joint probability that a Bachelors student prefers Documentaries?
3.54 What is the joint probability that a Masters student prefers watching News?
3.53 What is the joint probability that a Doctoral student prefers Documentaries?
3.52 What is the joint probability that a Doctoral student prefers Movies /Series?
3.40 A mail-order firm considers three possible events in filling an order:A: The wrong item is sent.B: The item is lost in transit.C: The item is damaged in transit.Assume that A is independent of both B and C and that B and C are mutually exclusive. The individual event probabilities are P1A2 =
3.37 It was estimated that 60% of all seniors on a campus were seriously concerned about employment prospects, 45% were seriously concerned about grades, and 30% were seriously concerned about both. What is the probability that a randomly chosen senior from this campus is seriously concerned about
3.32 The soccer league in one community has 7 teams. You are required to predict, in order, the top 5 teams at the end of the season. Ignoring the possibility of ties, calculate the number of different predictions you could make. What is the probability of making the correct prediction by chance?
3.28 A financial analyst was asked to evaluate earnings prospects for nine corporations over the next year, and rank them in order of predicted earnings growth rates.a. How many different rankings are possible?b. If, in fact, a specific ordering is the result of a guess, what is the probability
3.26 The probability of A is 0.70, the probability of B is 0.80, and the probability of both is 0.50. What is the conditional probability of A, given B? Are A and B independent in a probability sense?Application Exercises
3.22 The probability of event E is 0.54, the probability of event F is 0.38, and the probability of both is 0.2. What is the probability of either E and F?
3.21 The probability of A is 0.60, the probability of B is 0.40, and the probability of either is 0.76. What is the probability of both A and B?
3.20 The probability of A is 0.40, the probability of B is 0.45, and the probability of either is 0.85. What is the probability of both A and B?
3.19 The probability of A is 0.30, the probability of B is 0.70, and the probability of either is 0.90. What is the probability of both A and B?
3.17 A department store manager has monitored the number of complaints received per week about poor service.The probabilities for numbers of complaints in a week, established by this review, are shown in the following table. Let A be the event “there will be at least
3.16 If two events are mutually exclusive, we know that the probability of their union is the sum of their individual probabilities. However, this is not the case for events that are not mutually exclusive. Verify this assertion by considering the events A and B of Exercise 3.1.
3.15 A manager has available a pool of 12 employees who could be assigned to a project editorial task. Of the employees seven are women and five are men. Two of the men are brothers. The manager has to assign the project at random so that each of the 12 employees is equally likely to be chosen. Let
3.14 A fund manager is considering investing in a new software firm based in India. The manager’s assessment of probabilities for rates of return on this stock over the next year is summarized in the accompanying table. Let A be the event “rate of return will be at least 10%” and B be the
3.13 Sale manager wants to estimate a probability that a car will be returned for a service during the warranty period. The following table shows a manager’s probability assessment for the number of returns.Number of Returns (X) 0 1 2 3 4 Probability P(X) 0.28 0.36 0.23 0.09 0.04 Let A be the
3.12 In a city of 180,000 people there are 20,000 legal immigrants from Latin America. What is the probability that a random sample of two people from the city will contain two legal immigrants from Latin America?Application Exercises
3.11 In a city of 140,000 people there are 40,000 Norwegians.What is the probability that a randomly selected person from the city will be Norwegian?
3.10 The sample space contains 10 As and 6 Bs. What is the probability that a randomly selected set of 4 will include 2 As and 2 Bs?
3.9 The sample space contains 8 As and 6 Bs. What is the probability that a randomly selected set of 3 will include 2 As and 4 Bs?
3.8 The sample space contains 5 As and 7 Bs. What is the probability that a randomly selected set of 2 will include 1 A and 1 B?
3.5 A corporation takes delivery of some new machinery that must be installed and checked before it becomes available to use. The corporation is sure that it will take no more than 10 days for this installation and check to take place. Let A be the event“it will be more than 3 days before the
3.4 Given A = 3E3, E5, E7, E104 and B = 3E3, E4, E5, E94a. What is the intersection of A and B?b. What is the union of A and B?c. Is the union of A and B collectively exhaustive?Application Exercises
3.3 Given A = 3E1, E4, E5, E74 and B = 3E2, E3, E5, E84a. What is A intersection B?b. What is A intersection B?c. What is the union of A and B?d. Is the union of A and B collectively exhaused?
3.2 Given A = 3E1, E3, E6, E94 , define A.
3.1 the sample space S = 3E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E114 . Given A = 3E5, E6, E7, E84 and B = 3E5, E7, E9, E114a. What is A intersection B?b. What is the union of A and B?c. Is the union of A and B collectively exhaustive?For Exercises 3.2–3.4 use the sample space S defined as
3.5 Bayes’ Theorem Subjective Probabilities in Management Decision Making
3.4 Bivariate Probabilities Odds Overinvolvement Ratios
3.3 Probability Rules Conditional Probability Statistical Independence
3.2 Probability and Its Postulates Classical Probability Permutations and Combinations Relative Frequency Subjective Probability
3.1 Random Experiment, Outcomes, and Events
2.56 Management of a local retail outlet in Australia wants to predict weekly online shopping sales. It administers an aptitude test to all sales people, where test scores range from 0 to 10 with greater scores indicating a higher aptitude. Test scores and weekly sales (in AU$000) are as
2.55 To explore the relationship between the grades students receive on their first quiz (X) and their first exam (Y). The first quiz and exam scores for a sample of students reveal the following data:Quiz Scores (x) 4 3.4 3 5 1.1 Exam Scores (y) 78 66 82 80 30a. Compute the covariance.b. Compute
2.54 How much time (in minutes) do people spend on a typical visit to a local mall? A random sample of n = 104 shoppers was timed and the results (in minutes)are stored in the data file Shopping Times.You were asked to describe graphically the shape of the distribution of shopping times in Exercise
2.49 Consider the following four populations:• 2, 3, 4, 5, 5, 6, 7, 8• 1, 1, 1, 4, 5, 7, 7, 14• 2, 4, 4, 5, 5, 8, 8, 4• -9, -3, 0, 3, 9, 12, 13, 15 All these populations have the same mean. Without doing the calculations, arrange the populations according to the magnitudes of their
2.47 The following data represents the age of the students enrolled at a music school and the scores obtained by them in an entrance exam. The scores ranged from 0 to 70. Describe the data numerically.15, 402 19, 652 112, 482 19, 662 18, 462 16, 562 17, 642 110, 572 111, 422 112, 692 19, 532 17,
2.44 A local bus company wants to estimate if the major travel line from a local city to the capitol is a profitable route. The number of passengers and the number of corresponding trips made during a two-month period are recorded in the following table:Passengers 0 6 10 10 6 20 20 6 30 30 6 40 40
2.43 The president of World Aircraft Association wants to determine if there is a relationship between the number of vacation days provided to cabin crew members of eight airline companies and their monthly salaries (in thousands of euros). He obtained the following random sample on the number of
2.42 The farmer based in Gujarat, India, wants to determine the relationship between the number of rainy days in August and the amount of rice (kg) sold per month.Data was collected for a 5-year period are as follows:11, 402 10, 322 13, 362 18, 442 15, 412 The first number indicates the number of
2.41 A professor at the University of Oulu, Finland, keeps records of the number of hours each student studies and the grades they receive. A random sample of hours studied and test grades for n = 11 contracts is stored in the data file Oulu Grades.a. Compute the covariance.b. Compute the
2.40 The manager of a used-car dealership is very interested in the resale price of used cars. The manager feels that the age of the car is important in determining the resale value. He collects data on the value of the car (in thousands of dollars) as the dependent variable and the age of the car
2.39 Travel Shaw is an agency based in Bulgaria that employs a group of travel reporters who publish stories based on exciting destinations from around the world.Travel Shaw also offers three destination tours: Asia, Europe, and the United States. One of the agents at Travel Shaw wants to determine
2.38 According to Statista, in 2016, global retail sales of chocolate amounted to approximately $98.2 billion, making choclates one of the most popular snacks in the world. A random sample of 15 consumers were given varying quantities of chocolates for four weeks. The following (x, y) data shows
2.37 According to the Office for National Statistics (ONS), the monthly growth rate in the quantity of goods bought in Great Britain increased by 1.0% in January 2019, after a 0.7% decline in December 2018.Source: Office for National Statistics, “Retail sales, Great Britain: January 2019,”
2.36 Following is a random sample of seven (x, y) pairs of data points:111, 1022 115, 512 16, 252 114, 302 110, 212 18, 562 113, 302a. Compute the covariance.b. Compute the correlation coefficient.
2.35 Following is a random sample of 11 (x, y) pairs of data points:115, 452 16, 182 111, 332 112, 362 116, 482 114, 422 15, 152 117, 512 14, 122 119, 572 17, 212a. Compute the covariance.b. Compute the correlation coefficient.
2.33 The number of problems solved on the entrance exam is given in the table:Number of Exams 0 1 2 3 4 Number of Problems 100 110 130 50 10 Find the mean and standard deviation of the number of problems per exam.
2.32 For predicting credit default, a sample of 20 financial data analysts was asked to provide forecasts of credit scores for next year. The results are summarized in the following table:Forecast (£ 000) Number of Clients 10.95 6 11.45 5 11.45 6 12.95 18 12.95 6 13.45 16 13.45 6 14.95 23 14.95 6
2.31 A survey was conducted to find the amount of money university students spend during Valentine's day. A random sample of 28 students was selected from a local university in Brussels and their responses are recorded in the following table:Money Spent (€) 20 13 10 5 0 Number of students 2 8 8 6
2.30 Frequent-flyer programs are customer loyalty programs used by many passenger airlines.The following table shows the number of award trips offered to 60 passengers during the last year.Number of Award Trips 0 1 2 3 4 5 Number of Passengers 21 12 8 9 6 4a. Find the mean number of the award trips
2.29 An online-grocery market is growing fast. A sample of 40 customers is selected and the number of online orders over the last month are listed in the following table.Number of Orders 0 1 2 3 Number of Customers 12 13 9 6 Calculate the standard deviation.
2.28 A drive-through fast-food chain obtained the following pick-up times (number of minutes between the time an order is placed and the time the order is picked up at the drive-through window). A random sample of 30 orders along with the corresponding duration is given in the following
2.27 Consider the following frequency distribution for a sample of 40 observations:Class Frequency 0 6 5 5 5 6 10 6 10 6 15 12 15 6 20 10 20 6 25 7a. Calculate the sample mean.b. Calculate the sample variance and sample standard deviation.Application Exercises
2.26 Consider the following sample of five values and corresponding weights:xi wi 4.7 8 3.8 7 5.7 4 2.6 3 5.5 2a. Calculate the arithmetic mean of the xi values without weights.b. Calculate the weighted mean of the xi values.
2.22 According to CleanTechnica website, Sweden’s full electric vehicles took a record high 24.1%share of new sales, with the Kia e-Niro being Sweden’s best-selling full electric vehicle. Suppose you are an employee at a Kia showroom in Sweden. Your manager asks for an overview of the range
2.21 Navigating through an airport can be quite chaotic.You could instead choose to spend your waiting time at one of the airport lounges—hospitality areas where you can relax and enjoy food and beverages before you jet off. A random sample of 10 airport lounges are selected and the following

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Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

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