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mathematics
business statistics

Questions and Answers of Business Statistics

Boxer A is favored to win over boxer B with odds 4:3. Simulate nine rounds between the two and declare a winner.
A sales representative finds that there is a 30% probability of making a sale by visiting the potential customer personally. For every 20 calls, find the probability of making three sales in a row.
Find a study that uses a questionnaire. Select any questions that you feel are improperly written.
A basketball player has a 60% success rate for shooting foul shots. If she gets two shots, find the probability that she will make one or both shots.
A field goal kicker is successful in 60% of his kicks inside the 35-yard line. Find the probability of kicking three field goals in a row.
Many research studies described in newspapers and magazines do not report the sample size or the sampling method used. Try to find a research article that gives this information; state the sampling
In Exercise 19, find the average number of shots fired.In Exercise 19Two shooters shoot clay pigeons. Gail has an 80% accuracy rate and Paul has a 60% accuracy rate. Paul shoots first. The first
Four dice are rolled 50 times. Find the average of the sum of the number of spots that will appear.
Select a cluster of 10 states, and compute the mean number of electoral votes for the sample. Compare this mean with the population mean. States and number of electoral votes for each AL GA 16 AK 3
Two shooters shoot clay pigeons. Gail has an 80% accuracy rate and Paul has a 60% accuracy rate. Paul shoots first. The first person who hits the target wins. Find the probability that each wins.
To win a certain lotto, a person must spell the word big. Sixty percent of the tickets contain the letter b, 30% contain the letter i, and 10% contain the letter g. Find the average number of tickets
A football is placed on the 10-yard line, and a team has four downs to score a touchdown. The team can move the ball only 0 to 5 yards per play. Find the average number of times the team will score a
Select a systematic sample of 10 states, and compute the mean number of electoral votes for the sample. Compare this mean with the population mean. States and number of electoral votes for each AL
The probability that a door is locked is 0.6, and there are five keys, one of which will unlock the door. The experiment consists of choosing one key at random and seeing if you can unlock the door.
Choose a different method to select 10 states and compute the sample mean high temperature. Compare with your answer in Exercise 15 and with the population mean. Do you see any features of this data
A caramel corn company gives four different prizes, one in each box. They are placed in the boxes at random. Find the average number of boxes a person needs to buy to get all four prizes.
Which method of sampling might be good for this set of data? Choose one to select 10 states and calculate the sample mean. Compare with the population mean. Record high temperatures AL 112 MT 117 AK
A die is rolled until all faces appear at least once. Find the average number of tosses.
Are there any characteristics of these data that might create problems in sampling? Average population State Pupils per teacher AL 15.9 47,949 65,468 49,885 AK 13.3 AZ 17.5 AR 15.0 46,631 69,324
Select a cluster sample of 10 states, and find the mean of the average population and the mean of the pupils per teacher. How do your results compare with the U.S. figures? Average population State
Select a systematic sample of 10 states, and find the mean of the average population and the mean of the pupils per teacher. How do your results compare with the U.S. figures? Average population
Using the table of random numbers, select 10 states and find the mean of the average population and the mean of the pupils per teacher. How do your results compare with the U.S. figures? Average
Select a cluster sample of 10 states, and find the mean of the unemployment rates and the mean of the average weekly benefits. How do your results compare with the U.S. figures? A verage weekly
Find the mean of the unemployment rates and the mean of the average weekly benefits. How do your results compare with the U.S. figures? A verage weekly benefit ($) State Unemployment rate (%) AL 6.5
Select a systematic sample of 10 states, and find the mean of the unemployment rates and the mean of the average weekly benefits. How do your results compare with the U.S. figures? A verage weekly
Select a random sample of 10 states, and find the mean of the unemployment rates and the mean of average weekly benefits. How do your results compare with the U.S. figures? A verage weekly benefit
Divide the 23 storms into 4 subgroups (The fourth group will only have 5 storms.). Then select a sample of three storms from each group. Compute the means for wind speeds. Compare these means to the
Select a cluster of 10 storms. Compute the sample means wind speeds. Compare these sample means with the population means. Atlantic or Classification Name Max. wind Pacific Ana 60 Bill 60 A
Select a systematic sample of eight storms and calculate the average maximum wind speed. Compare with the population mean. Atlantic or Classification Name Max. wind Pacific Ana 60 Bill 60 A
Give three examples of simulation techniques.
Select a random sample of eight storms by using random numbers, and find the average maximum wind speed. Compare with the population mean. Atlantic or Classification Name Max. wind Pacific Ana 60
Toss a coin 30 times and record the outcomes (H or T). Test the results for randomness at α = 0.05. Repeat the experiment a few times and compare your results.
Select a three-digit state lottery number over a period of 50 days. Count the number of times each digit, 0 through 9, occurs. Test the claim, at α = 0.05, that the digits occur at random.
Give three examples of proportions.
Conduct a survey of the number of extracurricular activities your classmates are enrolled in. Construct a probability distribution and find the mean, variance, and standard deviation.
Roll two dice 100 times and find the mean, variance, and standard deviation of the sum of the dots. Compare the result with the theoretical results obtained in Exercise 20.In exerciseConstruct a
Select a newspaper or magazine article that involves a statistical study, and write a paper answering these questions.a. Is this study descriptive or inferential? Explain your answer.b. What are the
Find an article that describes a statistical study, and identify the study as observational or experimental.
Find a gambling game and explain how probability was used to determine the outcome.
Find three statistical studies and explain whether they used descriptive or inferential statistics.
In a newspaper or magazine of your choice, find a statistical study that contains an estimated population proportion.
Give an example of interest to you for comparing two population means. Identify the variable under consideration and the two populations.
In a current newspaper or magazine, find two examples of graphs that might be misleading. Explain why you think the graphs are potentially misleading.
Class Project: Number of Siblings. This exercise is a class project and works best in relatively large classes.a. Determine the number of siblings for each student in the class.b. Obtain a
In a newspaper or magazine, or on the Internet, find an example of a. A descriptive study.b. An inferential study.
Given A = {1, 4, 7}, B = {3, 4, 6, 8, 9} and C = {1, 3, 4, 5, 6, 7}, solve the following.(a) A ∪ B = __________(b) A ∩ C = __________(c) B ∩ C = __________(d) A ∪ B ∪ C =
Determine a possible frame for conducting random sampling in each of the following studies.(a) The average amount of overtime per week for production workers in a plastics company in Queensland.(b)
The Land Transport Safety Authority of New Zealand conducted a survey on public attitudes to road safety and found that 78% of New Zealanders agreed that New Zealand roads are safer to travel on.
A study by the ASX reveals that 39% of the Australian adult population are shareholders. In addition, the study determines that 7.1% of all Australian adult shareholders have postgraduate education.
Determine the mean, variance and standard deviation of the following discrete distribution. Explain the results.x ........................... P(x)0 ...........................0.0911
Solve the following problems by using the binomial formula.(a) If n = 5 and p = 0.10, find P(x = 2).(b) If n = 8 and p = 0.80, find P(x = 5).(c) If n = 10 and p = 0.70, find P(x ≥ 6).(d) If n = 13
Solve the following problems by using the binomial tables (table A.1 in the appendix).(a) If n = 20 and p = 0.50, find P(x = 12).(b) If n = 20 and p = 0.30, find P(x > 8).(c) If n = 20 and p =
Find the mean and standard deviation of the following binomial distributions.(a) n = 20 and p = 0.70(b) n = 70 and p = 0.35(c) n = 100 and p = 0.50
A survey of holiday accommodation in New Zealand shows that in Auckland, excluding caravan parks and camping grounds, 42% were full (i.e. had no vacancies). A random sample of 25 holiday
A survey conducted by Certified Practising Accountants Australia to investigate the reaction to new audit standards issued by the Auditing and Assurance Standards Board finds that only 53% of
The normal distribution can model many real-world characteristics that can be measured. Explain why the height of 18-year-old boys, the volume contained in 2-litre bottles of a particular brand of
Free-range eggs are produced on a farm. The weight of these eggs is found to be normally distributed with a mean of 55 g and standard deviation of 1 g. Using the empirical rule and no calculations,
Using σ = 25 and σ = 3, calculate the corresponding z-scores for each of the following values of x.(a) 16(b) 20(c) 24(d) 28
Using σ = 100 and σ2 = 25, calculate the corresponding z-scores for each of the following values of x.(a) 85(b) 92(c) 103(d) 113
Determine the probability for the following intervals of the standard normal distribution.(a) z ≥ 1.96(b) z < 0.73(c) –1.46 < z ≤ 2.84(d) –2.67 ≤ z ≤ 1.08(e) –2.05 < z ≤
A survey shows that one in five people aged 16 years or older do some volunteer work. If this figure holds for the entire population and if a random sample of 150 people aged 16 years or older is
Truck freight delivery times between Brisbane and Sydney have been found to be approximately normally distributed. If the average freight delivery time is 12.5 hours with a standard deviation of 0.45
The values of investment properties in Brisbane are normally distributed with mean $360 000 and standard deviation $60 000. An investment property is randomly selected.(a) What is the probability
The age of real estate investors is found to be normally distributed with a mean of 40 years and a standard deviation of 10 years. What proportion of investors are below the age of 25?
According to the Department of Building and Housing, the average rent for a one-bedroom Auckland City apartment is NZ$314 with a standard deviation of $88. Given that rents are normally distributed,
Consider the average home loan in New Zealand of $283 000, where the standard deviation is $50 000 and home loans are normally distributed.(a) What proportion of home loans are more than $250 000?(b)
The weights of a medium-sized loaf of homemade bread in Australia, using high-grade baking flour and a bread-making machine, have been found to be normally distributed with an average weight of 750 g
It is estimated that the cost of running a small car is $150 per week, based on driving 15 000km per year. Taking the cost to be normally distributed with a standard deviation of $10 per week, answer
The average speeds of passenger trains travelling from Kyoto to Tokyo have been found to be normally distributed with a mean of 250 km per hour and standard deviation of 30 km per hour. What is the
Solve the following problems, assuming that the data are normally distributed.(a) The standard deviation of the distribution is 12.56, and 71.97% of the values are greater than 56. What is the value
Determine whether the following binomial distributions can be adequately approximated by a normal distribution.(a) p = 0.1, n = 10(b) p = 0.2, n = 30(c) p = 0.6, n = 15(d) p = 0.8, n = 15(e) p = 0.9,
If each of the following binomial distributions can be approximated by a normal distribution, what are the values of the mean and standard deviation?(a) p = 0.2, n = 25(b) p = 0.5, n = 25(c) p = 0.7,
In the TV game show The Price is Right, two contestants spin a wheel that is divided into 100 equal segments numbered 1 to 100. After each contestant spins the wheel and it stops, the one who lands
In the TV game show Temptation, one of the temptations is the ‘temptation vault’, in which the leading contestant presses a buzzer to win a dollar amount from $1 up to $10000. What is the
ABS data show that young full-time students work an average of 15 hours per week. If the number of hours worked is normally distributed with this mean and 10% of students work more than 25 hours a
Let x follow an exponential distribution. Determine the following probabilities.(a) P(x ≥ 5 | ???? = 1.35)(b) P(x < 3 | ???? = 0.68)(c) P(x > 4 | ???? = 1.7)(d) P(x < 6 | ???? = 0.80)
During the dry month of December, Perth has measurable rain on average for only 2 days of the month. If the arrival of rainy days is Poisson distributed in Perth during the month of December, what is
(a) A study is to be conducted to look at consumer gambling habits in the horseracing industry.(b) A local government wants to understand the attitudes of its ratepayers. A representative community
The mean of a population is 54 and the standard deviation is 10. The shape of the population is unknown. Determine the probability of each of the following occurring for this population.(a) A random
List some strata into which each of the following variables can be divided.(a) Employee qualification(b) Company value(c) Car park size(d) Degree program studied by university students(e) Job
Forty-six per cent of a population possesses a particular characteristic. Random samples are taken from this population. Determine the probability of each of the following occurrences.(a) The sample
Suppose the age distribution in a city is as follows.Age ......................... PercentageUnder 18 .................... 16%18–25 .......................... 19%26–50 ..........................
If a university employed 3500 academic staff and a random sample of 175 academic staff was selected using systematic sampling, what value of k was used? Between what two values would the sampling
For each of the following research projects, list at least one area or cluster that could be used in obtaining the sample.(a) A study of road conditions in the North Island of New Zealand(b) A study
A population is normally distributed with a mean of 14 and a standard deviation of 1.2. What is the probability of each of the following?(a) Taking a sample of 26 and obtaining a sample mean of 13.7
Give an example of how convenience sampling could be used in a study of Australian Financial Review Top 1000 CEOs to measure corporate attitudes towards paternity leave for employees.
A population has a mean of 150 and a standard deviation of 21. If a random sample of 49 is taken, what is the probability that the sample mean is:(a) Greater than 154(b) Less than 153(c) Less than
The Department of Housing can provide apartment accommodation in a particular city. The average cost of renting a two-bedroom apartment in this city is $800 per month. What is the probability of
According to the ABS, the average length of stay by tourists in Queensland’s hotels, motels and serviced apartments is 2.2 days with a standard deviation of 1.2 days. A sample of 65 randomly
According to ABS figures, average weekly total earnings of all employees in Australia is $1179 per week. Take this population standard deviation to be $45 per week. If a representative random sample
A new housing estate contains 1500 houses. A sample of 100 houses is selected randomly and evaluated by a real estate agent. If the mean appraised value of a house for all houses in this area is
The monthly mobile phone bill for all customers at a large telecommunications company is found to be normally distributed with a mean of $145.55 per month and standard deviation of $15.22 per month.
It is estimated that 80% of occupants use electricity as their main source of heating during winter in newly constructed apartments in Auckland. A random sample of 100 apartments is selected to
A recent survey of Australians found that mean sleep time was 8 hours with a standard deviation of 3 hours. Assume sleep time is normally distributed. What is the probability that:(a) A randomly
For a population with p = 0.6, find the probability for each sample proportion and given sample size.(a) n = 12 and p̂ < 0.77(b) n = 30 and p̂ > 0.56(c) n = 65 and 0.54 < p̂ < 0.56(d)
A population proportion is 0.32. Suppose a random sample of 40 items is sampled randomly from this population. What is the probability that the sample proportion is:(a) Greater than 0.42(b) Between
According to a study undertaken in a large rural town, 15% of children aged from 10 to 16 years were found to exercise less than one hour per day. If a random sample of 35 children in this age group
Use these data to construct 90%, 95% and 99% confidence intervals to estimate ?. Assume ? is 4.9. State the point estimate.
Use the following information to construct the confidence intervals specified to estimate µ.(a) 99% confidence for X̅ = 35, σ = 5.2 and n = 55(b) 95% confidence for X̅ = 85, σ = 6.3 and n =
A company sells 25 g boxes of sultanas that are promoted as a healthy snack food option for children. The company wants to estimate the number of sultanas packed into a box. To do so, a random sample

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