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business statistics using excel
Basic Business Statistics Concepts And Applications 5th Edition L. Berenson Mark, David Levine, Kathryn Szabat, Judith Watson, Nicola Jayne, Martin O'brien - Solutions
In Example 5.4 three friends went to a Hungry Jack’s franchise.Instead, suppose that they go to a McDonald’s franchise, which last month filled 90% of orders correctly.a. What is the probability that:i. all three orders will be filled correctly?ii. none of the three will be filled
A student taking a multiple-choice test consisting of five questions, each with four options, selects the answers randomly. What is the probability that the student will get:a. five questions correct?b. at least four questions correct?c. no questions correct?d. no more than two questions correct?
Research has shown that only 60% of consumers read every word, including the fine print, of a service contract. Assume that the number of consumers who read every word of a contract can be modelled using the binomial distribution. A group of five consumers has just signed a 12-month contract with
The increase or decrease in the price of a share between the beginning and the end of a trading day is assumed to be an equally likely random event. What is the probability that a share will show an increase in its closing price on five consecutive days?
Suppose that in problem 5.13 you wanted to create a portfolio that consists of a corporate bond fund and a common share fund.a. Calculate the portfolio expected return and portfolio risk for each of the following percentages invested in a corporate bond fund:i. 30%ii. 50%iii. 70%b. On the basis of
You are trying to set up a portfolio that consists of a corporate bond fund and a common share fund. The following information about the annual return (per $1,000) of each of these investments under different economic conditions is available, together with the probability that each of these
Suppose that in problem 5.11. you wanted to create a portfolio that consists of share X and share Y.a. Calculate the portfolio expected return and portfolio risk for each of the following percentages invested in share X:i. 30%ii. 50%iii. 70%b. On the basis of the results of your calculations in
You are developing a strategy for investing in two different shares. The anticipated annual return for a $1,000 investment in each share has the following probability distribution:
The process of being served at a bank consists of two independent parts – the time waiting in line and the time it takes to be served by the teller. Suppose, at a branch of Check$mart, that the time waiting in line has an expected value of 4 minutes with a standard deviation of 1.2 minutes and
Two investments, X and Y, have the following characteristics:E(X ) = $50, E(Y ) = $100, σX 2 = 9,000, σY 2 = 15,000 and σXY = 7,500 If the weight assigned to investment X of portfolio assets is 0.4, calculate:a. the portfolio expected returnb. the portfolio risk
Given the following probability distributions for variables X and Y:P(Xi Yi) X Y 0.2 -100 50 0.4 50 30 0.3 200 20 0.1 300 20 Calculate:a. E(X ) and E(Y )b. σX and σYc. σXYd. E(X + Y )
Given the following probability distributions for variables X and Y:P(Xi Yi) X Y 0.4 100 200 0.6 200 100 Calculate:a. E(X ) and E(Y )b. σX and σYc. σXYd. E(X + Y )
In the casino version of the traditional Australian game of two-up, a spinner stands in a ring and tosses two coins into the air. The coins may land showing two heads, two tails or one tail and one head (odds). Players can bet on either heads or tails at odds of one to one. Therefore, if a player
The manager of a large computer network has developed the following probability distribution of the number of interruptions per day:
Using the company records for the past 500 working days, the manager of Konig Motors has summarised the number of cars sold per day in the following table:a. Form the probability distribution for the number of cars sold per day.b. Calculate the mean or expected number of cars sold per day.c.
Are each of the following a valid probability distribution? Justify your answers:
Given the following probability distributions:a. Calculate the expected value for each distribution.b. Calculate the standard deviation for each distribution.
In a town, 45% of all households have a pet, 35% have children, and 40% of all households with children have a pet.Using these definitions:P 5 event household has a pet C 5 event household has childrena. Complete the following contingency table.
The following table classifies residents of a regional area of Queensland by gender, age and hours of unpaid domestic work in the week before the 2016 Census.
The following table classifies residents of a regional area of New South Wales by gender and age.
A researcher has completed a survey of 10,000 New Zealand viewers to determine which channel they watch on a weekday during the 6.30 pm to 7.30 pm time-slot, with the following results:
The employees of a company were surveyed and asked their educational background and marital status. Of the 600 employees, 400 had university degrees, 100 were single and 60 were single university graduates.a. Construct a contingency table for this problem.b. Find the probability that a randomly
In an online test, 10 multiple-choice questions are randomly selected from a test bank of 100 questions.a. If the order in which the questions appear is immaterial, how many different tests can be generated?b. If the order in which the questions appear is important, how many different tests can be
In a certain region, during a recent outbreak of a preventable disease 0.1% of primary school children caught the disease; of these 30% were vaccinated against it. Furthermore, of those who did not catch the disease 80% were vaccinated.a. What percentage of vaccinated children caught the disease?b.
When calculating premiums on life insurance products insurance companies often use life tables that enable the probability of a person dying in any age interval to be calculated.
In March 2013, 26.8% of New South Wales dwellings suitable for a rainwater tank had one installed. Of the dwellings with a rainwater tank, 53.1% had the rainwater tank plumbed into the dwelling (Australian Bureau of Statistics, Environmental Issues: Water Use and Conservation, Mar 2013, Cat. No.
The Melbourne Cup, held on the first Tuesday in November, has 24 horses entered in it.
In a school of 200 students 95% are vaccinated against a certain disease. During a recent outbreak of this disease 20 students, including 11 vaccinated students, developed the disease.a. Find the probability that a student i. who has the disease has been vaccinated ii. who has been vaccinated
The breakdown by home address of the previous year’s 993 drink-driving offences in Problem 2.67 is:
What is the difference between a permutation and a combination?
How can you use Bayes’ theorem to revise probabilities in light of new information?
How does the multiplication rule differ for events that are and are not independent?
How does conditional probability relate to the concept of statistical independence?
What is the difference between mutually exclusive events and collectively exhaustive events?
How can you use the addition rule to find the probability of occurrence of event A or B?
What is the difference between a simple event and a joint event?
What are the differences between a priori classical probability, empirical classical probability and subjective probability?
Find an example online or in print of an unethical or misleading use of probability.
Write an advertisement for:a. Lotto that ethically describes the probability of winningb. the investment newsletter that ethically states the probability of a 20% return
A reading list for a unit contains 20 articles. How many ways are there to choose three articles from this list?
A daily lottery is conducted in which two winning numbers are selected out of 100 numbers.a. How many different combinations of winning numbers are possible?b. Suppose that you have an entry in this lottery – what is your probability of winning?
Nine passengers are on a waiting list for an overbooked flight. Due to cancellations, four seats are available. How many ways are there, regardless of order, to allocate the four seats?
A trifecta consists of picking the correct finishing order of the first three horses in a race. Suppose 12 horses are entered in a race.a. How many trifecta outcomes are there for this race?b. If you choose three horses randomly, what is the probability that you win the trifecta?
Each employee of a large firm has an ID number consisting of their initials (either two or three) followed by two digits. What is the maximum number of unique ID numbers generated by this system?
Currently, new standard New South Wales vehicle number plates consist of two letters followed by two digits followed by two letters. How many possible number plates are there of this form?
If each letter is used once, how many different arrangements are there of:a. Grafton?b. Otaki?c. Darwin?d. Gore?
Greenway Gardens has a $10 salad box consisting of lettuce, tomatoes, cucumber, sprouts, capsicum, avocado and a bottle of Greenway’s special salad dressing. Suppose that at present there is a choice of eight types of lettuce, four types of tomatoes, three types of cucumbers, three types of
A particular brand of women’s jeans is available in seven different sizes, three different colours and three different styles.How many different jeans does the store manager need to order to have one pair of each type?
A lock on a bank vault consists of three dials, each with 30 positions. To open the vault, each of the three dials must be in the correct position.a. How many different possible dial combinations are there for this lock?b. What is the probability that, if you randomly select a position on each
If there are 10 multiple-choice questions in an exam, each with three possible answers:a. How many different answer sequences are there?b. If you answer the questions randomly, what is the probability that you get all 10 correct?
From past records of personal loans the Check$mart Bank found that 10% of borrowers default on their loan – that is, they fail to pay. It also found that, of those who default, 32% are unemployed while, of those who do not default, only 2% are unemployed.a. What percentage of unemployed borrowers
The editor of a textbook-publishing company is trying to decide whether to publish a proposed business statistics textbook.Information on previous textbooks published indicate that 10%are huge successes, 20% are modest successes, 40% break even and 30% are failures. However, before a publishing
An advertising executive is studying the television viewing habits of married men and women during prime-time hours. On the basis of past viewing records, the executive has determined that, during prime time, husbands are watching television 60%of the time. When the husband is watching television,
In Example 4.10 on page 165, suppose that the probability that the test will return a false positive (that is, the medical diagnostic test gives a positive result when the disease is not present) is reduced from 0.02 to 0.01. Given this information:a. If the medical diagnostic test has given a
If P(B) 5 0.30, P(A | B) 5 0.60 and P(A | B′) 5 0.50, find P(B | A).
If P(B) 5 0.05, P(A | B) 5 0.80 and P(A | B′) 5 0.40, find P(B | A).
A standard deck of cards is being used to play a game. There are four suits (hearts, diamonds, clubs and spades), each having 13 faces (ace, 2 to 10, jack, queen and king), making a total of 52 cards. This complete deck is thoroughly shuffled, and you will receive the first two cards from the deck
In 59 of the 88 years from 1929 to 2016, the S&P 500 (Standard and Poor’s 500 Index, one of the indices of the New York Stock
A study was done to determine the efficacy of three different headache tablets – A, B and C. One thousand study participants used all three tablets (at different times) over the period of the study with the following results:
A sample of 500 consumers was selected in a large metropolitan area to study consumer behaviour with the following results:
At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male.a. What is the probability that a student selected at random in the university is a male in the business
Households in a certain town were surveyed to determine whether they would subscribe to a new Pay TV channel. The households were classified according to ‘high’, ‘medium’ and‘low’ income levels. The results of the survey are summarised in the table below.
The following table gives the labour force status of the Australian civilian population aged 15 years and over in May 2017:
If P (A) 5 0.3, P (B) 5 0.4, and P (A and B) 5 0.2, are A and B statistically independent?
If P (A) 5 0.7, P (B) 5 0.6, and A and B are statistically independent, find P (A and B).
If P (A and B) 5 0.4 and P (B) 5 0.8, find P (A | B).
Given the following contingency table:
Given the following contingency table:
A sample of 500 consumers is selected in a large metropolitan area to study consumer behaviour. Among the questions asked was ‘Do you enjoy shopping for clothing (Yes or No)?’ Of 240 males, 136 answered yes. Of 260 females, 224 answered yes. Construct a contingency table or a Venn diagram to
A researcher has completed a survey of 10,000 viewers in a regional city to determine which TV network they watch most weekdays during the 6 pm to 7 pm time slot. The results are
The probability of each of the following events is zero. For each, state why.a. A day is Christmas and Easter.b. A product is defective and not defective.c. A car is a Ford and a Toyota.
For each of the following, state whether the events are mutually exclusive and/or collectively exhaustive. If they are not mutually exclusive and/or collectively exhaustive, either reword the categories to make them mutually exclusive and collectively exhaustive or explain why this would not be
For each of the following, indicate whether the type of probability involved is an example of a priori classical probability, empirical classical probability or subjective probability.a. The next toss of a fair coin will be heads.b. Italy will win soccer’s World Cup the next time the competition
Given the following contingency table:
Given the following contingency table:
An urn contains 12 red balls and 8 white balls. One ball is to be selected from the urn.a. Give an example of a simple event.b. What is the complement of a red ball?
Two coins are tossed.a. Give an example of a simple event.b. Give an example of a joint event.c. What is the complement of a head on the first toss?
Pre-numbered sales invoices are kept in a sales journal. The invoices are numbered from 0001 to 5,000.a. Beginning in row 16, column 1, and proceeding horizontally in Table E.1, select a simple random sample of 50 invoice numbers.b. Select a systematic sample of 50 invoice numbers. Use the random
A radio station survey of listeners found that 32% of the 1,356 drivers who responded admitted to talking on a hand-held mobile phone while driving, and 23% admitted to reading or sending SMS messages while driving. What information would you want to know before you accepted the results of the
The results of the 2017 Adobe Mobile Maturity Survey reveal insights into the change to smartphones as primary online access devices, and indicate the need for companies to focus on creating engaging and personalised digital experiences for their customers. How are companies addressing the mobile
Alex and Tyler have been monitoring their electricity use since installing solar power almost a year ago, with the data stored in < SOLAR_POWER > .Explore Alex and Tyler’s power usage over this period by:a. plotting the data graphicallyb. calculating summary statisticsc. commenting on the graphs
< GDP > gives the annual percentage change in real gross domestic product (GDP) per quarter since 2000 for New Zealand (NZ), Australia, the United States of America (USA), Japan and the United Kingdom (UK) (data obtained from Reserve Bank of New Zealand accessed 1 June 2017).a. Investigate the
An economist exploring the relationship between interest rates and inflation has collected interest and CPI data from the reserve banks of New Zealand and Australia for 2000 to March 2017 (data obtained from Reserve Bank of Australia and Reserve Bank of New Zealand < www.rba.gov.au> and accessed 1
Several hundred laboratory tests are performed at a large hospital each day. The rate at which these tests are done improperly (and therefore need to be redone) seems steady, at about 4%. In an effort to get to the root cause of these nonconformances (tests that need to be redone), the director of
For the previous year a large confectionary chain, Sweets-4-U, is interested in analysing the quantity sold weekly, including associated cost data, of two of its popular products, ‘Forgive’and ‘Rejoice’.These products, both wrapped chocolates sold by weight, differ only in the message
One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in a car. The steel is cut with a diamond saw and the resulting parts must be within ±0.125 mm of the length specified by the car manufacturer.The data in < STEEL > come from a sample
The file < AGE > contains the ages and gender of the Australian population at 30 June 2013 and 2016.a. Construct percentage and cumulative percentage distributions for the age of males, females and the entire Australian population in 2013 and 2016.b. Construct and interpret appropriate graphs to
The call centre supervisor of the IT helpdesk of a large university is monitoring the performance of the technical support staff. The data in the file < HELP_DESK > give the number of calls resolved during a random sample of 20 eighthour shifts by five support staff.a. For each staff member,
If two students receive a mark of 90 on the same examination, what arguments could be used to show that the underlying variable – test score – is continuous?
The data in < PROBLEMS > are random samples of the time (in minutes) taken to resolve 40 problems reported by students and 40 problems reported by staff to the Technology Services(TS) Service Desk at Tasman University.For each sample:a. Construct appropriate tables and/or charts to investigate the
The following table gives the results on food groups never eaten from a national study of 10,000 men and 10,000 women aged at least 50. < FOOD >a. For men and women, separately and combined, construct percentage summary tables and bar charts for the data.b. What conclusions can you draw about the
Comment on the following graph, which appeared in the Northern Star in August 2008.
The following data represent the amount of soft drink filled in a sample of 50 consecutive 2-litre bottles. The results are listed horizontally in the order filled. < DRINK >a. Construct a frequency distribution and a percentage distribution.b. Plot a histogram and a percentage polygon.c. Form a
To test the effectiveness of mail X-ray screening in identifying potential illegal or threatening items a mail centre X-rays a random sample of 500 packages and then independently searches each package. The results of this test are given below.
The table below classifies the academic staff of a small regional university by gender and level.< ACADEMIC_STAFF >a. Illustrate these data by constructing appropriate tables and graphs.b. What can you conclude about gender and level for academic staff at this university?c. Estimate the mean and
The file < CURRENCY > contains the monthly closing exchange rates for the New Zealand dollar (NZD), the Japanese yen (JPY), the United States dollar (USD) and the Chinese renminbi (CNY)from January 2010 to May 2017, where each currency is expressed in units per Australian dollar (data obtained from
For each of the following variables, determine whether the variable is categorical or numerical. If the variable is numerical, determine whether it is discrete or continuous. In addition, determine the level of measurement.a. Amount of money spent on clothing in the last monthb. Favourite
The data below represent the distribution of the ages of employees in two different divisions of a publishing company.
The data in the file < NZ_CAR_SALES_16_17 > are of sales of new cars in New Zealand for February 2016 and 2017 (data obtained from Motor Industry Association of New Zealand accessed 27 March 2017). For each year, ignoring the other category:a. Calculate the mean, variance and standard deviation for
The data stored in data file < WEBSTATS > classify the number of times, during August and September, that a sample of 50 students accessed a statistics unit website by day and time.a. Construct appropriate tables and/or charts to investigate the day of the week and the time that students access the
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