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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
A market researcher states that she has 95% confidence that the mean monthly sales of a product are between $170,000 and $200,000. Explain the meaning of this statement.
If X– = 125, σ = 24 and n = 36, construct a 99% confidence interval estimate of the population mean μ.
If X– = 85, σ = 8 and n = 64, construct a 95% confidence interval estimate of the population mean μ.
The council for a regional city constructed a levee to protect the central business district and surrounding suburbs from flooding in up to a 1-in-10-year flood. This levee was finished 12 years ago, and has just been breached for the first time, having held during three previous floods.Assume that
The manager of a seafood restaurant was interested in studying ordering patterns of patrons for the Friday-to-Sunday weekend time period. Records were maintained that indicated the demand for dessert during the same period. The manager decided to study two other variables together with whether a
Refer to problem B.57.a. For cinemas, using the given probability of attendance of 0.663, calculate the probability that, of the 10 people sampled, the number who have attended a cinema in the past year is:i. exactly none ii. all 10 iii. more than half iv. eight or moreb. Compare the results in (a)
Refer to problem B.57. Calculate the probability that, of the 10 people sampled, the number who have attended a musical or opera in the past year is:a. exactly noneb. all 10c. more than halfd. eight or more
Australia is known as a nation of sports lovers but cultural events and venues are not all well supported. A survey by the Australian Bureau of Statistics found that in 2013–14 the attendance rates for Australians aged 15 years and over at the following selected cultural events and venues were as
Sam and Jo recently lost their house to fire. Although they were insured, the insurance company has offered them 30% less than the rebuild amount for which they were insured.The amount for which they were insured was the amount specified by the insurance company and is consistent with the rebuild
Jay has had three incidents in the past 10 years where an insurance excess needed to be paid. These were a collision with a kangaroo, hail damage and a collision from behind while stationary. In this last instance the excess was refunded as the other driver was at fault. Furthermore, Jay estimates
Assume that in 2018 the manufacturers of brand H improve their performance, with owners of 2018 brand H reporting 1.04 problems per car.a. If you purchased a 2018 brand H, what is the probability that the new car will have:i. zero problems?ii. two or fewer problems?b. Compare your answers in part
A motoring organisation has conducted a survey of owners of new cars manufactured in 2017. It has listed the average number of problems per car as 1.27 for brand H. Let the random variable X be equal to the number of problems with a newly purchased brand H.a. What assumptions must be made in order
According to Burton G. Malkiel, the daily changes in the closing price of shares follow a random walk – that is, these daily events are independent of each other and move upwards or downwards in a random manner – and can be approximated by a normal distribution.To test this theory, use either a
In problem 6.12 on page 229, it was assumed that the number of All Ordinaries shares traded daily on the Australian Securities Exchange (ASX) is a normal random variable.a. To test this assumption use the All Ordinaries daily volume of trade for the 2016–17 financial year< ALL_ORDS_2016_17 >
In the Household Expenditure Statistics: Year Ended 30 June 2016 (Statistics New Zealand, , licensed by Statistics New Zealand for re-use under the Creative Commons Attribution 3.0 New Zealand licence), 64% of the New Zealand households reported that their income was enough or more than enough to
Past records show that on average there are four unplanned outages a year to Check$mart’s Internet banking system and that these unplanned outages occur randomly and are independent of each other.An unplanned outage has just occurred.a. What is the probability that there will:i. not be an
Check$mart encourages its customers to use Internet banking.Therefore the bank is concerned with the download time (the number of seconds that passes from first linking to the website until the home page is fully displayed) of its home page. Both the design of a home page and the load on the
A telemarketing firm phones households at random. Data show that 80% of such calls are answered.a. If 100 households are called each evening, approximate the probability that:i. more than 50% of the calls are answered ii. between 70 and 90 (inclusive) calls are answered iii. fewer than 75 calls are
In 2015, 16.4% of Australians aged 45 to 54 years reported a disability compared to 8.2% aged 15 to 24 years (data obtained from Australian Bureau of Statistics, Disability, Ageing and Carers, Australia: Summary of Findings, 2015, Cat. No. 4430.0 ).Suppose 15 Australians in each age group are
Data from the Bureau of Infrastructure, Transport and Regional Economics (BITRE) () shows that in Australia during 2015, the number of motorcyclist deaths was 6.47 per 100 million vehicle kilometres travelled (VKT), while for car occupants it was 0.35 per 100 million VKT.A local council estimates
A manager of a seafood restaurant is interested in both the time it takes a customer to be seated (the waiting time) and the length of time between a customer being seated and leaving the restaurant (the service time). Over a month, a random sample of 100 customers (only one per party/table)was
The amount of time a bank teller spends with each customer has a population mean μ = 3.10 minutes and standard deviation σ = 0.40 minute.a. If you select a random sample of 16 customers:i. what is the probability that the mean time spent per customer is at least 3 minutes?ii. there is an 85%
A small factory processes and bottles fruit juice. Two types of defect can occur – an incorrect fill amount (over or under the stated amount on the label) and an incorrect seal.From production data it is known that 0.5% of two-litre bottles filled have an incorrect fill amount and 0.1% are
An airline maintains statistics for mishandled bags per 1,000 passengers. Suppose that last year this airline had 7.03 mishandled bags per 1,000 passengers. What is the probability that the next 1,000 passengers on this airline will have:a. no mishandled bags?b. at least one mishandled bag?c. at
Olive Construction Company is determining whether it should submit a bid for a new shopping centre. In the past, Olive’s main competitor, Base Construction Company, has submitted bids 70% of the time. If Base Construction does not bid on a job, the probability that Olive Construction will get the
Greenway Gardens currently has six plots available to plant tomatoes, eggplant, capsicum, cucumbers, beans and lettuce.Each vegetable will be planted in one and only one plot. How many ways are there to position these vegetables in the gardens?
Assume that the number of network errors experienced in a day on a local area network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 2.4. What is the probability that, in any given day:a. zero network errors will occur?b. exactly one
Suppose that a quality control department has established that 0.1% of items produced are defective.a. If 25 items are randomly selected, find the probability that:i. exactly two items are defective ii. at most one item is defective iii. at least two items are defectiveb. What is the expected
A quinella consists of picking the horses that will place first and second in a race irrespective of order. Suppose eight horses are entered in a race.a. How many quinella combinations are there for this race?b. If you choose two horses randomly, what is the probability that you win the quinella?
A research institute has interviewed a total of 1,764 employers.Fifty-three per cent of the 264 employers from the telecommunications industry expected to have a net increase in employment in their company during the next quarter. Only 43% of employers interviewed from other industries expected a
One theory concerning the Standard & Poor’s (S&P) 500 Index of US stocks is that if it increases during the first five trading days of the year, it is likely to increase during the entire year.From 1929 to 2016, early gains during the first five days predicted full-year gains approximately 69.5%
The cost of a phone call passed on to a ‘live’ operator is approximately 10 times that of a call answered by an automated customer-service system. However, as more and more companies have implemented automated systems, customer annoyance with these systems has grown. Many customers are quick to
Based on past experience, the owner of a stall at the local annual show states that 60% of visitors to the stall will purchase a showbag. On a certain day, the stall has 100 visitors.a. Is the 60% figure best classified as a priori classical probability, empirical classical probability or
A box of nine golf gloves contains two left-handed gloves and seven right-handed gloves.a. If two gloves are randomly selected from the box without replacement, what is the probability that both gloves will be right-handed?b. If two gloves are randomly selected from the box without replacement,
The Tasmanian Visitor Survey presents data in an analyser database on a number of aspects of tourism, including attractions visited by tourists aged 14 or over. The most visited attractions by 1,283,618 tourists in the October 2016 to September 2017 period were the Saturday Salamanca
At the local golf course golfers lose golf balls at a rate of 3.8 per 18-hole round. Assume that the number of golf balls lost in an 18-hole round is distributed as a Poisson random variable.a. What assumptions need to be made so that the number of golf balls lost in an 18-hole round is distributed
Based on past experience, 40% of all customers at Miller’s Service Station pay for their purchases with a credit card. If a random sample of 200 customers is selected, what is the approximate probability that:a. at least 75 pay with a credit card?b. not more than 70 pay with a credit card?c.
A particular weekly Bingo session consists of 20 games. In each game, there are two points where a player can win (a line and a house).Assume on a typical week that there are 100 players, each player is equally likely to win and winning is independent.a. Calculate the probability that a player has
A computer Help desk has two technicians, A with advanced training, who is able to solve 95% of problems, and B with less training, who is only able to solve 85% of problems. Each technician randomly receives 50% of problems.a. What percentage of solved problems are solved by technician A?b. What
On average 108 customers per hour join a queue at any one of the checkout counters of a grocery store. Suppose that the number of customers joining a queue at the checkout counters follows an approximate Poisson distribution.a. What is the probability that in the next minute:i. exactly four
The following table contains the probability distribution for the number of traffic accidents per day in a small city
In a recent opinion poll a sample of 1,200 adults (at least 20 years old) was surveyed. Of these adults, 768 were married, 684 were female and there were 459 married females.Construct a contingency table or a Venn diagram and evaluate the probability that a surveyed adult selected at random:a. is
An on-the-job injury occurs once every 10 days on average at a car manufacturer. What is the probability that the next on-the-job injury will occur within:a. 10 days?b. 5 days?c. 1 day?
Suppose the executive of the university in problem B.20 randomly select five senior (senior lecturer and above)academic staff members for a committee. Calculate the following probabilities:a. The selected members of the committee are all male senior lecturers.b. There are no professors on the
The table below classifies the academic staff of a small regional university by gender and level of appointment.
Of the packages searched at the mail centre in problem B.18, 9.6% are found to contain illegal or threatening items. Suppose 10 packages are independently and randomly selected to be searched.a. What is the probability that:i. exactly two contain illegal or threatening items?ii. none contain
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.
In each game of OZ Lotto seven numbers are selected from 1 to 45. To win the first-division prize, the seven winning numbers must have been selected. On any game, what is the probability of winning the first division?
On a tourism Twitter site, where photos of scenic views and native animals are regularly shared, the long-term average number of‘Likes’ obtained per photo posted is 600.5, with a standard deviation of 76. A sample of 52 photos is selected at random.a. What is the probability that the average
Telephone calls arrive at the information desk of a large computer software company at the rate of 15 per hour.a. What is the probability that the next call will arrive within 3 minutes (0.05 hour)?b. What is the probability that the next call will arrive within 15 minutes (0.25 hour)?c. Suppose
A survey of 1,500 students at a large university gave the following data on their study mode (full- or part-time) as well as their employment status.
At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This system raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10°C to 25°C.a. What is
Suppose that in problem B.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:
East Park Realty, a small real estate company located in country areas of South Australia, specialises primarily in
From a consignment of 64 large garden pots in individual crates being shipped from Vietnam to a local importer, 16 have imperfections such as cracks or are broken.a. If eight crates are shipped to a particular garden nursery, what is the probability that:i. all eight will have defective pots?ii.
It has been observed that 92% of train commuters travelling during the 8.00 am to 9.00 am period use a mobile phone during their trip for various activities.a. In a train carriage with 42 passengers during this period, what is the probability that fewer than 38 passengers use their mobile phone
An electrical retail store has found that 55% of its customers use a credit card to pay for their purchases.a. If 15 customers who make a purchase are randomly selected, what is the probability that:i. none use a credit card?ii. exactly five use a credit card?iii. more than two use a credit card?b.
The following data represent the electricity cost in dollars during the month of July for a random sample of 50 twobedroom apartments in a New Zealand city: < ELECTRICITY >96 171 202 178 147 102 153 197 127 82 157 185 90 116 172 111 148 213 130 165 141 149 206 175 123 128 144 168 109 167 95 163 150
The time between arrivals of cars at Sheng’s carwash is exponential with an average of 6 minutes between arrivals.What is the probability that the time between successive arrivals will bea. less than 2 minutes?b. more than 10 minutes?c. between 4 and 6 minutes?
a. If a coin is tossed seven times, how many different outcomes are possible?b. If a die is rolled seven times, how many different outcomes are possible?c. Discuss the differences in your answers to (a) and (b).
sets the filling machine so that the mean is 2.02 litres. Under these circumstances, what are your answers to (a) to (c)?
In an effort to reduce the number of bottles that contain less than 1.90 litres, the bottler in problem
The fill amount of soft-drink bottles is normally distributed with a mean of 2.0 litres (the listed content) and a standard deviation of 0.05 litre. Bottles that contain less than 95% of the listed net content (1.90 litres, in this case) make the manufacturer subject to penalties. Bottles that have
A soft-drink bottling company maintains records of the number of unacceptable bottles of soft drink coming from the filling and capping machines. Based on past data, the probability that a bottle came from machine I and was unacceptable is 0.01, and the probability that a bottle came from machine
(Class project ) Suppose that step 3 of problem 7.35 uses the following rule: ‘If a random digit between 0 and 8, inclusive, is selected, consider the ball to be white; if a random digit of 9 is selected, consider the ball to be red’. Compare and contrast the results in this problem and in
(Class project ) The table of random numbers can simulate the selection of different-coloured balls from a bowl as follows:1. Start in the row corresponding to the day of the month on which you were born.2. Select one-digit numbers.3. If a random digit between 0 and 6, inclusive, is selected,
(Class project ) Toss a coin 10 times and record the number of heads. If each student performs this experiment five times, a frequency distribution of the number of heads can be developed from the results of the entire class.Does this distribution seem to approximate the normal distribution?
(Class project ) The table of random numbers is an example of a uniform distribution because each digit is equally likely to occur. Starting in the row corresponding to the day of the month on which you were born, use the table of random numbers (Table E.1) to take one digit at a time.Select five
Assume that the returns for shares on the Chinese share market were distributed as a normal random variable, with a mean of 1.54 and a standard deviation of 10. If you select an individual share from this population, what is the probability that it would have a return:a. less than 0 (i.e. a
APRA, the Australian Prudential Regulation Authority, monitors the return rates of large superannuation funds in Australia. Its publication Statistics: Quarterly superannuation performance, December 2016 showed an annual rate of return of 6.8% for the year . Imagine that a researcher with access to
Assume that, for the first quarter of 2017, the weekly rental costs of three-bedroom dwellings in a coastal town in Western Australia are normally distributed with a mean of $260 and a standard deviation of $30. If you select a random sample of 10 dwellings from this population, what is the
A new online advertisement for an Extra Dry beer has been designed for a target audience of Australian males aged 18 to 30.The advertisers hope that 24% of the target audience will find the ad ‘very entertaining’. Suppose that a sample of 400 male television viewers in the target age group is
The ABS has reported that in 2015, 26.78% of the 16.8 million employees in Australia worked part-time in their main job(Australian Bureau of Statistics, Characteristics of Employment, Australia, August 2015, Cat. No. 6333.0, 2016). Suppose that you select a random sample of 250 employees from
The fill amount of milk in plastic containers is normally distributed with a mean of 2.0 litres and a standard deviation of 0.05 litres. If you select a random sample of 25 containers:a. What is the probability that the sample mean will be:i. between 1.99 and 2.0 litres?ii. below 1.98 litres?iii.
A particular type of ballpoint pen uses minute ball bearings that are targeted to have a diameter of 0.5 mm. The lower and upper specification limits under which the ball bearing can operate are 0.49 mm (lower) and 0.51 mm (upper). Past experience has indicated that the actual diameter of the ball
Under what circumstances does the sampling distribution of the proportion approximately follow the normal distribution?
What is the difference between a probability distribution and a sampling distribution?
Why does the sampling distribution of the mean follow a normal distribution for a large enough sample size even though the population may not be normally distributed?
Why does the standard error of the mean decrease as the sample size n increases?
Why is the sample mean an unbiased estimator of the population mean?
The 11th Annual Statistical Report of the HILDA Survey relates to the 2016 phase of a large longitudinal study of Australian residents. It found that 19.9% of households surveyed had HECS/HELP debts and 35.7% had debts on their home (R.Wilkins (ed), The Household, Income and Labour Dynamics in
The Australian Tax Office carries out a range of verification checks and audits for the goods and services tax (GST)including Business Activity Statement integrity audits. Assume that currently no additional tax is collected for 25% of such audits. Suppose that you select a random sample of 100
According to an Australian Government report, retail trade is the second largest employing industry in Australia with more than 1.267 million workers, or 11% of working Australians(Department of Employment, Australian Jobs 2016 accessed 28 April 2017). This report shows that the percentage of
As technology continues to change rapidly there has been a worldwide trend towards the use of smaller and more mobile devices and away from PCs. Analysts at Gartner predicted that in 2019 only 8% of devices shipped worldwide would be traditional PCs (desktops or notebooks)( accessed 27 April 2017).
People with permanent visas accounted for 19.5% of the net overseas migration to Australia during 2015. The relative shares of the different visa categories were: Family visas, 6.9%;Skilled, 9.0%; and Special Eligibility and Humanitarian, 2.5%(Australian Bureau of Statistics, Migration, Australia,
Over the past few years there has been increased monitoring of the representation of women on corporate boards. The Australian Institute of Company Directors reports in its March–May 2016 Report that 23.6% of ASX 200 board members were female ( accessed 25 April 2017).Suppose that the true
You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to identify correctly the brand they tasted. You select a random sample of 200 students and assume they have no ability to distinguish between the two brands. (Hint: If
A political polling organisation is conducting an analysis of sample results in order to make predictions on election night.Assuming a two-candidate election, if a specific candidate receives at least 55% of the vote in the sample, then that candidate will be forecast as the winner of the election.
The following data represent the responses (Y for yes and N for no) from a sample of 40 university students to the question, ‘Do you currently own any shares in listed companies?’:
A random sample of 50 households was selected for a telephone survey. The key question asked was, ‘Has any member of your household travelled by plane in the past month?’ Of the 50 respondents, 16 said yes and 34 said no. If the population proportion is 0.40:a. Determine the sample proportion p
In a random sample of 64 people, 48 are classified as‘successful’. If the population proportion is 0.70:a. Determine the sample proportion p of ‘successful’ people.b. Determine the standard error of the proportion.
A company is having a new corporate website developed. In the final testing phase the download time to open the new home page is recorded for a large number of computers in office and home settings. The mean download time for the site is 3.61 seconds. Suppose that the download times for the site
It is often important to monitor traffic on a website as organisations need to make online interactions with their clients faster and easier. For example, businesses applying for an Australian Business Number (ABN) online at are asked to have a variety of information about their entity ready before
Travel time on a bus between two suburban stops is normally distributed with μ = 8 minutes and σ = 2 minutes.a. If you select a random sample of 25 trips, what is the probability that the sample mean is between 6.9 and 8.2 minutes?b. If you select a random sample of 25 trips, what is the
Realestate.com.au reports that the median price of houses in the Newcastle suburb of Merewether that were sold in the 13 months to March 2017 was $1,150,000 (accessed 3 April 2017). Suppose that the mean price o houses in Merewether sold during that period was$1,236,450 and the standard deviation
The number of passengers passing through a large South East Asian airport is normally distributed with a mean of 110,000 persons per day and a standard deviation of 20,200 persons. If you select a random sample of 16 days:a. What is the sampling distribution of the mean?b. What is the probability
The following data represent the number of days absent per year in a population of six employees of a small company:1 3 6 7 9 10a. Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distribution of the mean. Calculate the mean of all the
For each of the following three populations, indicate what the sampling distribution of the mean for samples of 25 would consist of.a. Travel expense vouchers for a university in an academic yearb. Absentee records (days absent per year) in 2010 for employees of a large construction companyc.
Given a normal distribution with μ = 50 and σ = 5, if you select a sample of n = 100:a. What is the probability that X _is:i. less than 47?ii. between 47 and 49.5?iii. above 51.1?b. There is a 35% chance that X _is above what value?
Given a normal distribution with μ = 100 and σ = 10, if you select a sample of n = 25:a. What is the probability that X _is:i. less than 95?ii. between 95 and 97.5?iii. above 102.2?b. There is a 65% chance that X _is above what value?
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