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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+4. How many investors will she have to call, on average, to find someone interested?
=+3. How many people will she have to call until the probability of finding someone interested is at least 0.50?
=+2. What is the probability that none of the first five people she calls will be interested?
=+1. What is the probability that the first person she calls will want to invest?
=+Question 2: What is the probability that there are exactly 2 or 3 universal donors out of the 20 donors?
=+What are the mean and standard deviation of the number of universal donors?
=+c) What assumption did you make about the two customers in finding the standard deviation?
=+b) What’s the standard deviation of your wait time?
=+a) How long do you expect to wait for your turn to get tickets?
=+1 Suppose that the time it takes a customer to get and pay for seats at the ticket window of a baseball park is a random variable with a mean of 100 seconds and a standard deviation of 50 seconds. When you get there, you find only two people in line in front of you.
=+Assuming the two funds are independent, what are the relative advantages and disadvantages of putting $1000 into one, or splitting the $1000 and putting $500 into each? Compare the means and SDs of the profit from the two strategies.
=+A fund-raising lottery offers 500 tickets for $3 each. If the grand prize is $250 and 4 second prizes are $50 each, what is the expected value of a single ticket? (Don’t count the cost of the ticket in this yet.) Now, including its cost, what is the expected value of the ticket? (Knowing this
=+d) What is the mean time between arrivals?
=+c) What would the probability be that the time to the next arrival at the desk is 15 minutes or less?
=+b) What model would you use to model the time between arrivals at the information desk?
=+a) What model might you use to model the number of arrivals at this desk per hour?
=+66. Information desk. The arrival rate at a university library information desk is about 5 per hour, with an apparent lack of any relationship between arrivals in consecutive hours.
=+d) What is the probability that the time to the next purchase will be between 1 and 2 minutes?M07_SHAR8696_03_SE_C07.indd 268 14/07/14 7:31 AM Exercises 269
=+c) What is the mean time between purchases?
=+b) What model would you use to model the time between events?
=+a) What model might you suggest to model the number of purchases per minute?
=+65. Web visitors. A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of the others.
=+c) What did you assume to calculate b?
=+b) What is the probability he will still be at work at 5:45 PM every day this week (M-F)?
=+a) What is the probability he will still be at work at 5:45 PM?
=+64. Quitting time. My employee seems to leave work anytime between 5PM and 6PM, uniformly.
=+b) What is the probability that the fracture is found only after inspecting 16 km of the pipeline?
=+a) What is the probability that the fracture is found within the first stretch of 5 km?
=+63. Pipeline defects. Maintenance Engineers are responsible for the proper functioning of a 20 km long gas pipeline.If there is a pipeline failure, they need to physically inspect the whole stretch to discover the fracture. If X is how far the fracture is from them, X can be modeled as a uniform
=+62. Tennis. A tennis player has taken a special course to improve her serving. She thinks that individual serves are independent of each other. She has been able to make a successful first serve 70% of the time. Use a Normal approximation to find the probability she’ll make at least 65 of her
=+61. Rickets. Vitamin D is essential for strong, healthy bones. Although the bone disease rickets was largely eliminated in England during the 1950s, some people there are concerned that this generation of children is at increased risk because they are more likely to watch TV or play computer
=+60. Seatbelts. Police estimate that 80% of drivers wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. If they stop 120 cars, what’s the probability they find at least 20 drivers not wearing their seatbelt? Use a Normal approximation.
=+Normal approximation to find the probability that a righthanded student in one of these classes is forced to use a lefty arm tablet.
=+59. Lefties. A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The typical size of classes that meet there is 188, and we can assume that about 13% of students are left-handed. Use a
=+c) Suppose a customer puts a 20-pound weight at one end of the bar and the four 5-pound weights at the other end.Although he expects the two ends to weigh the same, they might differ slightly. What’s the probability the difference is more than a quarter of a pound?
=+b) It costs ABC $0.40 per pound to ship the box containing the weights. Because it’s an odd-shaped package, though, shipping the bar costs $0.50 a pound plus a $6.00 surcharge. Find the mean and standard deviation of the company’s total cost for shipping a starter set.
=+What’s the probability that the total weight in that second box exceeds 60.5 pounds? Define your variables clearly and state any assumptions you make.
=+a) ABC ships these starter sets to customers in two boxes:The bar goes in one box and the six weights go in another.
=+58. Weightlifting. The Atlas BodyBuilding Company (ABC)sells “starter sets” of barbells that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pounds. The weights average the specified amounts, but the
=+c) What’s the probability that on any given day he’ll sell a doughnut to more than half of his coffee customers?
=+b) If he makes a profit of 50 cents on each cup of coffee and 40 cents on each doughnut, can he reasonably expect to have a day’s profit of over $300? Explain.
=+a) The shop is open every day but Sunday. Assuming dayto-day sales are independent, what’s the probability he’ll sell more than 2000 cups of coffee in a week?
=+57. Coffee and doughnuts. At a certain coffee shop, all the customers buy a cup of coffee; some also buy a doughnut.The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 320 cups and a standard deviation of 20 cups. He also believes that the
=+d) If the next shipment is 40 bikes, what is the probability that the total set up cost will be less than $500?
=+c) Find the standard deviation of the set up cost.
=+b) Find the mean set up cost.
=+a) Define your random variables, and use them to express the total cost of the bike set up.
=+56. Bike sale. The bicycle shop in Exercise 55 estimates using current labor costs that unpacking a bike costs $0.82 on average with a standard deviation of $0.16. Assembly costs $8.00 on average with a standard deviation of $0.88 and tuning costs $4.10 with a standard deviation of $0.90.Because
=+b) A customer decides to buy a bike like one of the display models but wants a different color. The shop has one, still in the box. The manager says they can have it ready in half an hour. Do you think the bike will be set up and ready to go as promised? Explain.
=+a) What are the mean and standard deviation for the total bicycle setup time?
=+55. Bikes. Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take:• The times for each setup phase are
=+c) What’s the probability that your total expenses will exceed $400?
=+b) Describe the model for this total cost. Be sure to specify its name, expected value, and standard deviation.
=+a) Define appropriate variables and express the total annual veterinary costs you may have.
=+a cat. Assume that annual veterinary expenses are independent and have a Normal model with the means and standard deviations described in Exercise 52.
=+54. More pets. You’re thinking about getting two dogs and
=+c) If the weight of the remaining cereal can be described by a Normal model, what’s the probability that the box still contains more than 13 ounces?
=+a) Find the expected amount of cereal left in the box.
=+53. More cereal. In Exercise 51 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes is a random variable with mean 16.2 ounces and standard deviation 0.1 ounces.
=+d) What concerns do you have?
=+c) If the costs can be described by Normal models, what’s the probability that medical expenses are higher for someone’s dog than for her cat?
=+b) What’s the standard deviation of that difference?
=+a) What’s the expected difference in the cost of medical care for dogs and cats?
=+52. Pets. The American Veterinary Association claims that the annual cost of medical care for dogs averages $100, with a standard deviation of $30, and for cats averages$120, with a standard deviation of $35.
=+f) The amount of cereal the manufacturer puts in the boxes is a random variable with a mean of 16.3 ounces and a standard deviation of 0.2 ounces. Find the expected amount of cereal left in the box and the standard deviation.
=+e) If the total follows a Normal model, what’s the probability you poured out more than 4.5 ounces of cereal in the two bowls together?
=+d) What are the mean and standard deviation of the total amount of cereal in the two bowls?
=+c) If the difference follows a Normal model, what’s the probability the small bowl contains more cereal than the large one?
=+b) What’s the standard deviation of this difference?
=+a) How much more cereal do you expect to be in the large bowl?
=+51. Cereal. The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces.You open a new box of cereal and pour one large and one small bowl.
=+50. Stocks. A newsletter for investors recently reported that the average stock price for a blue chip stock over the past 12 months was $72. No standard deviation was given.Is the standard deviation more likely to be $6, $16, or $60?Explain.
=+49. CEOs. A business publication recently released a study on the total number of years of experience in industry among CEOs. The mean is provided in the article, but not the standard deviation. Is the standard deviation most likely to be 6 months, 6 years, or 16 years? Explain which standard
=+b) Which would be more unusual, a car traveling 34 mph or one going 10 mph?
=+a) How many standard deviations from the mean would a car going the speed limit be?
=+48. Car speeds. The police department of a major city needs to update its budget. For this purpose, they need to understand the variation in their fines collected from motorists for speeding. As a sample, they recorded the speeds of cars driving past a location with a 20 mph speed limit, a
=+b) Suppose those standard deviations are 1.5 months for the first company and 9 months for the second company.Does this change your opinion of the batteries? Explain.100.0% maximum 60 99.5% 60 97.5% 60 90.0% 60 75.0% quartile 60 50.0% median 53.5 25.0% quartile 17 10.0% 6.5 2.5% 0 0.5% 0 0.0%
=+a) Explain why you would also like to know the standard deviations of the battery life spans before deciding which brand to buy.
=+47. Claims. Two companies make batteries for cell phone manufacturers. One company claims a mean life span of 2 years, while the other company claims a mean life span of 2.5 years (assuming average use of minutes/month for the cell phone).
=+e) In planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the dealer does not want to take too big a risk. If the dealer is willing to give refunds to no more than 1 of every 25 customers, for what
=+d) Estimate the IQR for these data.
=+c) Approximately what fraction of these tires can be expected to last between 30,000 and 35,000 miles?
=+b) Approximately what fraction of these tires can be expected to last less than 30,000 miles?
=+a) If you buy a set of these tires, would it be reasonable for you to hope that they’ll last 40,000 miles? Explain.
=+46. Tire company. A tire manufacturer believes that the tread life of its snow tires can be described by a Normal model with a mean of 32,000 miles and a standard deviation of 2500 miles.
=+e) Above what value are the highest 15% of women’s cholesterol levels?
=+d) Estimate the interquartile range of the cholesterol levels.
=+c) What percent of adult women do you expect to have cholesterol levels between 150 and 170 mg>dL?
=+b) What percent of adult women do you expect to have cholesterol levels over 200 mg>dL?
=+45. Drug company. Manufacturing and selling drugs that claim to reduce an individual’s cholesterol level is big business. A company would like to market their drug to women if their cholesterol is in the top 15%. Assume the cholesterol levels of adult American women can be described by a
=+e) Explain the problem in using the Normal model for these data.
=+d) What percentage of students actually are within one standard deviation of the mean?
=+c) From a Normal model, about what percentage of students are within one standard deviation of the mean PR?
=+b) Which is a better summary of the spread, the IQR or the standard deviation? Explain.
=+a) Which is a better summary of the typical PR, the mean or the median? Explain.
=+44. Progress rate. Grade Point Average (GPA) and Progress Rate (PR) are two variables of crucial importance to students and schools. While each class’s GPA data is typically bell shaped, the PR data is quite different. Here is a histogram and summary statistics from a large class of business
=+c) Explain the problem in using the Normal model for these data.
=+b) For these data, what does that mean? Explain.
=+a) According to the Normal model, what percent of managers will exercise fewer than one standard deviation below the mean number of hours?
=+43. Management survey. A survey of 200 middle managers showed a distribution of the number of hours of exercise they participated in per week with a mean of 3.66 hours and a standard deviation of 4.93 hours.
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