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Applied Statistics In Business And Economics 4th Edition David Doane, Lori Seward - Solutions
As a birthday gift, you are mailing a new personal digital assistant (PDA) to your cousin in Toledo. The PDA cost $250. There is a 2 percent chance it will be lost or damaged in the mail. Is it worth $4 to insure the mailing? Explain, using the concept of expected value.
Use Excel to generate 1,000 random integers in the range 1 through 5.(a) What are the expected mean and standard deviation?(b) Show the Excel formula you used.
Consider the Bernoulli model. What would be a typical probability of success (π) for (a) Free throw shooting by a good college basketball player? (b) Hits by a good baseball batter? (c) Passes completed by a good college football quarterback? (d) Incorrect answers on a five-part multiple choice
There is a 14 percent chance that a Noodles & Company customer will order bread with the meal. Use Excel to find the probability that in a sample of 10 customers(a) More than five will order bread;(b) No more than two will;(c) None of the 10 will order bread.(d) Is the distribution skewed left
In a certain year, on average 10 percent of the vehicles tested for emissions failed the test. Suppose that five vehicles are tested.(a) What is the probability that all pass?(b) All but one pass?(c) Sketch the probability distribution and discuss its shape.
The probability that an American CEO can transact business in a foreign language is .20. Ten American CEOs are chosen at random.(a) What is the probability that none can trans- act business in a foreign language?(b) That at least two can?(c) That all 10 can?
In a certain Kentucky Fried Chicken franchise, half of the customers typically request "crispy" instead of "original."(a) What is the probability that none of the next four customers will request "crispy"?(b) At least two?(c) At most two?(d) Construct the probability distribution (Excel or Appendix
Oxnard Petro Ltd. is buying hurricane insurance for its off-coast oil drilling platform. During the next five years, the probability of total loss of only the above-water superstructure ($250 million) is .30, the probability of total loss of the facility ($950 million) is .30, and the probability
On average, 40 percent of U.S. beer drinkers order light beer.(a) What is the probability that none of the next eight customers who order beer will order light beer?(b) That one customer will?(c) Two customers?(d) Fewer than three?(e) Construct the probability distribution (Excel or Appendix A),
Write the Excel binomial formula for each probability.a. Three successes in 20 trials with a 30 percent chance of success.b. Seven successes in 50 trials with a 10 percent chance of success.c. Six or fewer successes in 80 trials with a 5 percent chance of success.d. At least 30 successes in 120
Tired of careless spelling and grammar, a company decides to administer a test to all job applicants. The test consists of 20 sentences. Applicants must state whether each sentence contains any grammar or spelling errors. Half the sentences contain errors. The company requires a score of 14 or
The default rate on government-guaranteed student loans at a certain private 4-year institution is 7 percent. The college extends 10 such loans.(a) What is the probability that none of them will default?(b) That at least three will default?(c) What is the expected number of defaults?
Experience indicates that 8 percent of the pairs of men's trousers dropped off for dry cleaning will have an object in the pocket that should be removed before cleaning. Suppose that 14 pairs of pants are dropped off and the cleaner forgets to check the pockets. What is the probability that no pair
A study by the Parents' Television Council showed that 80 percent of movie commercials aired on network television between 8 and 9 p.m. (the prime family viewing hour) were for R-rated lms.(a) Find the probability that in 16 commercials during this time slot at least 10 will be for R-rated lms.(b)
Write the Excel formula for each Poisson probability, using a mean arrival rate of 10 arrivals per hour.a. Seven arrivals.b. Three arrivals.c. Fewer than five arrivals.d. At least 11 arrivals.
A small feeder airline knows that the probability is .10 that a reservation holder will not show up for its daily 7:15 a.m. fight into a hub airport. The fight carries 10 passengers.(a) If the fight is fully booked, what is the probability that all those with reservations will show up?(b) If the
Although television HDTV converters are tested before they are placed in the installer's truck, the installer knows that 20 percent of them still won't work properly. The driver must install eight converters today in an apartment building.(a) Ten converters are placed in the truck. What is the
Why might the number of calls received per minute at a re station not be a Poisson event?
Find the mean and standard deviation of four-digit uniformly distributed lottery numbers (0000 through 9999).
Software filters rely heavily on "blacklists" (lists of known "phishing" URLs) to detect fraudulent e-mails. But such filters typically catch only 20 percent of phishing URLs. Jason receives 16 phishing e-mails.(a) What is the expected number that would be caught by such a filter?(b) What is the
Lunch customers arrive at a Noodles & Company restaurant at an average rate of 2.8 per minute. De ne X to be the number of customers to arrive during a randomly selected minute during the lunch hour and assume X has a Poisson distribution. (a) Calculate the probability that exactly five customers
In a major league baseball game, the average is 1.0 broken bat per game. Find the probability of (a) No broken bats in a game;(b) At least 2 broken bats.
In the last 50 years, the average number of deaths due to alligators in Florida is 0.3 death per year. Assuming no change in this average, in a given year find the probability of (a) No alligator deaths; (b) At least 2 alligator deaths.
In a recent year, potentially dangerous commercial aircraft incidents (e.g., near collisions) averaged 1.2 per 100,000 flying hours. Let X be the number of incidents in a 100,000-hour period.(a) Justify the use of the Poisson model.(b) What is the probability of at least one incident?(c) More than
At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 1.5 per day on a typical Wednesday. Let X be the number of cancellations on a particular Wednesday. (a) Justify the use of the Poisson model.(b) What is the probability that no cancellations will occur on a
Car security alarms go off at a mean rate of 3.8 per hour in a large Costco parking lot. Find the probability that in an hour there will be (a) No alarms; (b) Fewer than four alarms; and (c) More than five alarms.
In a certain automobile manufacturing paint shop, paint defects on the hood occur at a mean rate of 0.8 defect per square meter. A hood on a certain car has an area of 3 square meters. (a) Justify the use of the Poisson model. (b) If a customer inspects a hood at random, what is the probability
Past insurance company audits have found that 2 percent of dependents claimed on an employee's health insurance actually are ineligible for health benefits. An auditor examines a random sample of 7 claimed dependents. (a) What is the probability that all are eligible? (b) That at least one is
A "rogue wave" (one far larger than others surrounding a ship) can be a threat to ocean- going vessels (e.g., naval vessels, container ships, oil tankers). The European Centre for Medium-Range Weather Forecasts issues a warning when such waves are likely. The average for this rare event is
The ages of Java programmers at SynFlex Corp. range from 20 to 60.(a) If their ages are uniformly distributed, what would be the mean and standard deviation?(b) What is the probability that a randomly selected programmer's age is at least 40? At least 30?
In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.2 quakes per year. Let X be the number of quakes in a given year.(a) Justify the use of the Poisson model.(b) What is the probability of fewer than three quakes?(c) More than five quakes?(d) Construct the probability distribution
On New York's Verrazano Narrows bridge, traffic accidents occur at a mean rate of 2.0 crashes per day. Let X be the number of crashes in a given day.(a) Justify the use of the Poisson model.(b) What is the probability of at least one crash?(c) Fewer than five crashes? d) Construct the probability
Leaks occur in a pipeline at a mean rate of 1 leak per 1,000 meters. In a 2,500-meter section of pipe, what is the probability of (a) No leaks? (b) Three or more leaks? (c) What is the expected number of leaks?
Among live deliveries, the probability of a twin birth is .02. (a) In 200 live deliveries, how many would be expected to have twin births? (b) What is the probability of no twin births? (c) One twin birth? (d) Calculate these probabilities both with and without an approximation.
The probability is .03 that a passenger on United Airlines fight 9841 is a Platinum flyer (50,000 miles per year). If 200 passengers take this fight, use Excel to find the binomial probability of (a) No Platinum flyers, (b) One Platinum flyer, and (c) Two Platinum flyers. (d) Calculate the same
The probability of being "bumped" (voluntarily or involuntarily) on a U.S. airline was .00128. The average number of passengers traveling through Denver International Airport each hour is 5,708.(a) What is the expected number of bumped passengers per hour?(b) What is the approximate Poisson
On average, 2 percent of all persons who are given a breathalyzer test by the state police pass the test (blood alcohol under .08 percent). Suppose that 500 breathalyzer tests are given.(a) What is the expected number who pass the test?(b) What is the approximate Poisson probability that 5 or fewer
The probability of an incorrect call by an NFL referee is .025 (e.g., calling a pass complete, but the decision reversed on instant replays). In a certain game, there are 150 plays. (a) What is the probability of at least 4 incorrect calls by the referees? (b) Justify any assumptions that you made.
In CABG surgery, there is a .00014 probability of a retained foreign body (e.g., a sponge or a surgical instrument) left inside the patient.(a) In 100,000 CABG surgeries, what is the expected number of retained foreign bodies?(b) What is the Poisson approximation to the binomial probability of five
The probability of a job offer in a given interview is .25. (a) What is the expected number of interviews until the first job offer? (b) What is the probability the first job offer occurs within the first six interviews?
Flight 202 is departing Los Angeles. Is each random variable discrete (D) or continuous (C)? a. Number of airline passengers traveling with children under age 3. b. Proportion of passengers traveling without checked luggage. c. Weight of a randomly chosen passenger on Flight 202.
(a) At what x value does f (x) reach a maximum for a normal distribution N(75, 5)? (b) Does f (x) touch the X-axis at μ ± 3σ?
The probability that a certain kind of flower seed will germinate is .80.(a) If 200 seeds are planted, what is the probability that fewer than 150 will germinate?(b) That at least 150 will germinate?
On a cold morning the probability is .02 that a given car will not start in the small town of Eureka. Assume that 1,500 cars are started each cold morning.(a) What is the probability that at least 25 cars will not start?(b) More than 40?
At a certain re station, false alarms are received at a mean rate of 0.2 per day. In a year, what is the probability that fewer than 60 false alarms are received?
The HP dvd1040i 20X Multi format DVD Writer has an MTBF of 70,000 hours. (a) Assuming continuous operation, what is the probability that the DVD writer will last more than 100,000 hours? (b) Less than 50,000 hours? (c) At least 50,000 hours but not more than 80,000 hours? (Product specifications
Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.1 claim per month. (a) What is the probability that the dealership will wait at least 6 months until the next claim? (b) At least a year? (c) At least 2
Suppose the average time to service a Noodles & Company customer at a certain restaurant is 3 minutes and the service time follows an exponential distribution. (a) What is the probability that a customer will be serviced in less than 3 minutes? (b) Why is your answer more than 50 percent? Shouldn't
Systron Donner Inertial manufactures inertial subsystems for automotive, commercial/ industrial, and aerospace and defense applications. The sensors use a one-piece, microma-chined inertial sensing element to measure angular rotational velocity or linear acceleration. The MTBF for a single axis
The price (dollars per 1,000 board feet) of Douglas r from western Washington and Oregon varies according to a triangular distribution T(300, 350, 490).(a) Find the mean.(b) Find the standard deviation.(c) What is the probability that the price will exceed 400?
The distribution of scores on a statistics exam is T(50, 60, 95).(a) Find the mean.(b) Find the standard deviation.(c) Find the probability that a score will be less than 75.(d) Sketch the distribution and shade the area for the event in part (c).
The distribution of beach condominium prices in Santa Theresa ($ thousands) is T(500, 700, 2,100).(a) Find the mean.(b) Find the standard deviation.(c) Find the probability that a condo price will be greater than $750K.(d) Sketch the distribution and shade the area for the event in part (c).
State the Empirical Rule for a normal distribution.
On a police sergeant's examination, the historical mean score was 80 with a standard deviation of 20. Four officers who were alleged to be cronies of the police chief scored 195, 171, 191, and 189, respectively, on the test. This led to allegations of irregularity in the exam.(a) Convert these four
Discuss why you would or would not expect each of the following variables to be normally distributed. a. Shoe sizes of adult males. b. Years of higher education of 30-year-old employed women. c. Days from mailing home utility bills to receipt of payment. d. Time to process insurance claims for
Find the standard normal area for each of the following, showing your reasoning clearly and indicating which table you used. a. P (0 < Z < 0.50) b. P (–0.50 < Z < 0) c. P (Z > 0) d. P (Z = 0)
Find the standard normal area for each of the following, showing your reasoning clearly and indicating which table you used. a. P (1.22 < Z < 2.15) b. P (2.00 < Z < 3.00) c. P (–2.00 < Z 2.00) d. P (Z > 0.50)
Find the standard normal area for each of the following, showing your reasoning clearly and indicating which table you used. a. P (–1.22 < Z < 2.15) b. P (–3.00 < Z < 2.00) c. P (Z < 2.00) d. P (Z = 0)
Find the standard normal area for each of the following. Sketch the normal curve and shade in the area represented below. a. P (Z < – 1.96) b. P (Z > 1.96) c. P (Z < 1.65) d. P (Z > – 1.65)
Find the standard normal area for each of the following. Sketch the normal curve and shade in the area represented below. a. P (Z < –1.28) b. (P (Z >1.28) c. P (–1.96 < Z < 1.96) d. P (–1.65 < Z < 1.65)
Bob's exam score was 2.17 standard deviations above the mean. The exam was taken by 200 students. Assuming a normal distribution, how many scores were higher than Bob's?
Joan's finishing time for the Bolder Boulder 10K race was 1.75 standard deviations faster than the women's average for her age group. There were 405 women who ran in her age group. Assuming a normal distribution, how many women ran faster than Joan?
It is Saturday morning at Starbucks. Is each random variable discrete (D) or continuous (C)? a. Temperature of the coffee served to a randomly chosen customer. b. Number of customers who order only coffee with no food. c. Waiting time before a randomly chosen customer is handed the order.
Find the associated z-score for each of the following standard normal areas. a. Highest 10 percent b. Lowest 50 percent c. Highest 7 percent
Find the associated z-score for each of the following standard normal areas.a. Lowest 6 percentb. Highest 40 percentc. Lowest 7 percent
Find the associated z-score or scores that represent the following standard normal areas. a. Middle 50 percent b. Lowest 5 percent c. Middle 90 percent
Find the associated z-score or scores that represent the following standard normal areas.a. Middle 60 percentb. Highest 2 percentc. Middle 95 percent
Daily output of Marathon's Garyville, Lousiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels.(a) What is the probability of producing at least 232,000 barrels?(b) Between 232,000 and 239,000 barrels?(c) Less than
Assume that the number of calories in a McDonald's Egg McMuf n is a normally distributed random variable with a mean of 290 calories and a standard deviation of 14 calories. (a) What is the probability that a particular serving contains fewer than 300 calories? (b) More than 250 calories? (c)
The weight of a miniature Tootsie Roll is normally distributed with a mean of 3.30 grams and standard deviation of 0.13 gram.(a) Within what weight range will the middle 95 percent of all miniature Tootsie Rolls fall? Hint: Use the Empirical rule.(b) What is the probability that a randomly chosen
The pediatrics unit at Carver Hospital has 24 beds. The number of patients needing a bed at any point in time is N(19.2, 2.5). What is the probability that the number of patients needing a bed will exceed the pediatric unit's bed capacity?
Which of the following could not be probability density functions for a continuous random variable? Explain. a. f (x) = .25 for 0 ≤ x ≤ 1 b. f (x) = .25 for 0 ≤ x ≤ 4 c. f (x) = x for 0 ≤ x ≤ 2
The cabin of a business jet has a cabin height 5 feet 9 inches high. If a business traveler's height is N(59100, 2.70), what percentage of the business travelers will have to stoop?
On January 1, 2011, a new standard for baseball bat "liveliness" called BBCOR (Ball-Bat Coef-cient of Restitution) was adopted for teams playing under NCAA rules. A higher BBCOR allows the ball to travel farther when hit, so bat manufacturers want a high BBCOR. The maximum allowable BBCOR is 0.500.
Last year's freshman class at Big State University totaled 5,324 students. Of those, 1,254 received a merit scholarship to help offset tuition costs their freshman year (although the amount varied per student). The amount a student received was N($3,456, $478). If the cost of tuition was $4,200
The time required to verify and fill a common prescription at a neighborhood pharmacy is normally distributed with a mean of 10 minutes and a standard deviation of 3 minutes. Find the time for each event. Show your work. a. Highest 10 percent b. Middle 50 percent c. Highest 80 percent d. Lowest 10
The time required to cook a pizza at a neighborhood pizza joint is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes. Find the time for each event. Show your work. a. Highest 5 percent b. Lowest 50 percent c. Middle 95 percent d. Lowest 80 percent
The weight of a McDonald's cheeseburger is normally distributed with a mean of 114 ounces and a standard deviation of 7 ounces. Find the weight that corresponds to each event. Show your work.a. Highest 5 percent b. Lowest 50 percent c. Middle 95 percentd. Lowest 80 percent
The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 360 grams and a standard deviation of 9 grams. Find the weight that corresponds to each event. Show your work.a. Highest 10 percent b. Middle 50 percent c. Highest 80 percentd. Lowest 10 percent
The weights of newborn babies in Foxboro Hospital are normally distributed with a mean of 6.9 pounds and a standard deviation of 1.2 pounds. (a) How unusual is a baby weighing 8.0 pounds or more? (b) What would be the 90th percentile for birth weight? (c) Within what range would the middle 95
The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 600 and a standard deviation of 100.(a) Find the credit score that defines the upper 5 percent.(b) Seventy-five percent of the customers will have a credit score higher
The number of patients needing a bed at any point in time in the pediatrics unit at Carver Hospital is N(19.2, 2.5). Find the middle 50 percent of the number of beds needed (round to the next higher integer since a "bed" is indivisible).
For a continuous PDF, why can't we sum the probabilities of all x-values to get the total area under the curve?
Vail Resorts pays part-time seasonal employees at ski resorts on an hourly basis. At a certain mountain, the hourly rates have a normal distribution with 5 $3.00. If 20 percent of all part-time seasonal employees make more than $13.16 an hour, what is the average hourly pay rate at this mountain?
The average cost of an IRS Form 1040 tax ling at Thetis Tax Service is $157.00. Assuming a normal distribution, if 70 percent of the lings cost less than $171.00, what is the standard deviation?
Use Excel to find each probability. a. P(X < 110) for N(100, 15) b. P(X < 2.00) for N(0, 1) c. P(X < 5,000) for N(6000, 1000) d. P(X < 450) for N(600, 100)
Use Excel to find each probability. a. P(80 < X < 110) for N(100, 15) b. P(1.50 < X < 2.00) for N(0, 1) c. P(4,500 < X < 7,000) for N(6000, 1000) d. P(225 < X < 450) for N(600, 100)
The weight of a small Starbucks coffee is a normal random variable with a mean of 360 g and a standard deviation of 9 g. Use Excel to find the weight corresponding to each percentile of weight. a. 10th percentile b. 32nd percentile c. 75th percentile d. 90th percentile e. 99.9th percentile f.
A study found that the mean waiting time to see a physician at an outpatient clinic was 40 minutes with a standard deviation of 28 minutes. Use Excel to find each probability. (a) What is the probability of more than an hour's wait? (b) Less than 20 minutes? (c) At least 10 minutes.
High-strength concrete is supposed to have a compressive strength greater than 6,000 pounds per square inch (psi). A certain type of concrete has a mean compressive strength of 7,000 psi, but due to variability in the mixing process it has a standard deviation of 420 psi. Assume a normal
The default rate on government-guaranteed student loans at a certain public four-year institution is 7 percent.(a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults?(b) More than 100? Show your work carefully.
In a certain store, there is a .03 probability that the scanned price in the bar code scanner will not match the advertised price. The cashier scans 800 items.(a) What is the expected number of mismatches? The standard deviation?(b) What is the probability of at least 20 mismatches?(c) What is the
The probability is .90 that a vending machine in the Oxnard University Student Center will dispense the desired item when correct change is inserted. If 200 customers try the machine, find the probability that(a) At least 175 will receive the desired item and(b) That fewer than 190 will receive the
Find the mean and standard deviation for each uniform continuous model.a. U (0, 10)b. U (100, 200)c. U (1, 99)
When confronted with an in-fight medical emergency, pilots and crew can consult staff physicians at a global response center located in Arizona. If the global response center is called, there is a 4.8 percent chance that the fight will be diverted for an immediate landing. Suppose the response
On average, 28 patients per hour arrive in the Foxboro 24-Hour Walk-in Clinic on Friday between 6 p.m. and midnight.(a) What is the approximate probability of more than 35 arrivals?(b) What is the approximate probability of fewer than 25 arrivals?(c) Is the normal approximation justified? Show all
For a large Internet service provider (ISP), web virus attacks occur at a mean rate of 150 per day.(a) Estimate the probability of at least 175 attacks in a given day.(b) Estimate the probability of fewer than 125 attacks.(c) Is the normal approximation justified? Show all calculations.(d) Use
In Santa Theresa, false alarms are received at the downtown re station at a mean rate of 0.3 per day.(a) What is the probability that more than 7 days will pass before the next false alarm arrives?(b) Less than 2 days?
Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders per hour. Find the probability that(a) At least 30 minutes will elapse before the next telephone order;(b) Less than 15 minutes will elapse; and(c) Between 15 and 30 minutes will elapse.
A passenger metal detector at Chicago's Midway Airport gives an alarm 2.1 times a minute. What is the probability that (a) less than 60 seconds will pass before the next alarm? (b) More than 30 seconds? (c) At least 45 seconds?
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