High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 20 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
> J.D. Power and Associates says that 60 percent of car buyers now use the Internet for research and price comparisons. (a) Find the probability that in a sample of 8 car buyers, all 8 will use the Internet; (b) at least 5; (c) more than 4. (d) Find the me
> Popcorn kernels are believed to take between 100 and 200 seconds to pop in a certain microwave. (a) Estimate σ using Method 3 from Table 8.11. (b) What sample size (number of kernels) would be needed to estimate the true mean seconds to pop wi
> Last year, a study showed that the average ATM cash withdrawal took 65 seconds with a standard deviation of 10 seconds. The study is to be repeated this year. How large a sample would be needed to estimate this year’s mean with 95 percent confidence and
> A random survey of 500 students was conducted from a population of 2,300 students to estimate the proportion who had part-time jobs. The sample showed that 245 had part-time jobs. Calculate the 90 percent confidence interval for the true proportion of st
> A survey showed that 4.8 percent of the 250 Americans surveyed had suffered some kind of identity theft in the past 12 months. (a) Construct a 99 percent confidence interval for the true proportion of Americans who had suffered identity theft in the past
> Of 43 bank customers depositing a check, 18 received some cash back. (a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (b) Check the normality assumption of p.
> From a list of stock mutual funds, 52 funds were selected at random. Of the funds chosen, it was found that 19 required a minimum initial investment under $1,000. (a) Construct a 90 percent confidence interval for the true proportion requiring an initial
> In a sample of 500 new websites registered on the Internet, 24 were anonymous (i.e., they shielded their name and contact information). (a) Construct a 95 percent confidence interval for the proportion of all new websites that were anonymous. (b) May nor
> A car dealer is taking a customer satisfaction survey. Find the margin of error (i.e., assuming 95% confidence and π = .50) for (a) 250 respondents, (b) 125 respondents, and (c) 65 respondents.
> Find the margin of error for a poll, assuming that π = .50. a. n = 50 b. n = 200 c. n = 500 d. n = 2,000
> Should p be assumed normal? a. n = 25, π = .50 b. n = 60, π = .20 c. n = 100, π = .08
> 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 approximati
> Should p be assumed normal? a. n = 200, π = .02 b. n = 100, π = .05 c. n = 50, π = .50
> Calculate the standard error of the sample proportion. a. n = 40, π = .30 b. n = 200, π = .10 c. n = 30, π = .40 d. n = 400, π = .03
> Calculate the standard error of the sample proportion. a. n = 30, π = .50 b. n = 50, π = .20 c. n = 100, π = .10 d. n = 500, π = .005
> A random sample of 10 shipments of stick-on labels showed the following order sizes. (a) Construct a 95 percent confidence interval for the true mean order size. (b) How could the confidence interval be made narrower? (Data are from a project by MBA stud
> A random sample of monthly rent paid by 12 college seniors living off campus gave the results below (in dollars). Find a 99 percent confidence interval for μ, assuming that the sample is from a normal population. 900 810 770 860 850 79
> A sample of 21 minivan electrical warranty repairs for “loose, not attached” wires (one of several electrical failure categories the dealership mechanic can select) showed a mean repair cost of $45.66 with a standard deviation of $27.79. (a) Construct a
> Find the interval within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population. a. μ = 200, σ = 12, n = 36 b. μ = 1,000, σ = 15, n = 9 c. μ = 50, σ = 1, n = 25
> For each value of d.f. (degrees of freedom), look up the value of Student’s t in Appendix D for the stated level of confidence. Then use Excel to find the value of Student’s t to four decimal places. Which method (Appendix D or Excel) do you prefer, and
> Find a confidence interval for μ assuming that each sample is from a normal population. a. x bar = 24, s = 3, n = 7, 90 percent confidence b. x bar = 42, s = 6, n = 18, 99 percent confidence c. x bar = 119, s = 14, n = 28, 95 percent confidence
> The Ball Corporation’s beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000959 mm. If a random sample of 58 sheets of metal resulted in x = 0.2731 mm, c
> 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)
> Guest ages at a Vail Resorts ski mountain typically have a right-skewed distribution. Assume the standard deviation (σ) of age is 14.5 years. (a) Even though the population distribution of age is right skewed, what will be the shape of the distribution o
> The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5-speed using premium fuel is normally distributed with a known standard deviation of 1.25 MPG. If a random sample of 10 tanks of gas yields a mean of 21.0 MPG, find the 95 percent co
> A random sample of 100 items is drawn from a population whose standard deviation is known to be σ = 50. The sample mean is x bar = 850. a. Construct an interval estimate for μ with 95 percent confidence. b. Repeat part a assuming that σ = 100. c. Repeat
> A random sample of 25 items is drawn from a population whose standard deviation is known to be σ = 40. The sample mean is x bar = 270. a. Construct an interval estimate for μ with 95 percent confidence. b. Repeat part a assuming that n = 50. c. Repeat pa
> Use the sample information x bar = 37, σ = 5, n = 15 to calculate the following confidence intervals for μ assuming the sample is from a normal population: (a) 90 percent confidence; (b) 95 percent confidence; (c) 99 percent confidence. (d) Describe how
> Construct a confidence interval for μ assuming that each sample is from a normal population. a. x bar = 24, σ = 3, n = 10, 90 percent confidence b. x bar = 125, σ = 8, n = 25, 99 percent confidence c. x bar = 12.5, σ = 1.2, n = 50, 95 percent confidence
> If all normal distributions have the same shape, how do they differ?
> Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 2,500 pounds to 4,500 pounds. (a) What is the mean weight of a randomly chosen vehicle? (b) The standard deviation? (c) What is the prob
> For a continuous uniform distribution, why is P(25 < X < 45) the same as P(25 < X < 45)?
> Suppose that the distribution of oil prices ($/bbl) is forecast to be T(50, 65, 105). (a) Find the mean. (b) Find the standard deviation. (c) Find the probability that the price will be greater than $75. (d) Sketch the distribution and shade the area for
> When confronted with an in-flight 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 flight will be diverted for
> Suppose that the distribution of order sizes (in dollars) at L.L. Bean has a distribution that is T(0, 25, 75). (a) Find the mean. (b) Find the standard deviation. (c) Find the probability that an order will be less than $25. (d) Sketch the distribution
> The Johnson family uses a propane gas grill for cooking outdoors. During the summer they need to replace their tank on average every 30 days. At a randomly chosen moment, what is the probability that they can grill out (a) at least 40 days before they ne
> 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?
> In Santa Theresa, false alarms are received at the downtown fire 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? (c) Explain fully.
> Find the mean and standard deviation for each uniform continuous model. a. U (0, 10) b. U (100, 200) c. U (1, 99)
> 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 dev
> 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 minu
> 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)
> The average cost of an IRS Form 1040 tax filing at Thetis Tax Service is $157.00. Assuming a normal distribution, if 70 percent of the filings cost less than $171.00, what is the standard deviation?
> 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).
> 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 it
> On January 1, 2011, a new standard for baseball bat “liveliness” called BBCOR (Ball-Bat Coefficient 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 hig
> 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?
> Assume that the number of calories in a McDonald’s Egg McMuffin 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 c
> The fastest 10 percent of runners who complete the Nosy Neighbor 5K race win a gift certificate to a local running store. Assuming a normal distribution, how many standard deviations below the mean must a runner’s time be in order to win the gift certifi
> 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
> State the Empirical Rule for a normal distribution.
> (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?
> 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 chos
> 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
> 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 probabi
> A lottery ticket has a grand prize of $28 million. The probability of winning the grand prize is .000000023. Based on the expected value of the lottery ticket, would you pay $1 for a ticket? Show your calculations and reasoning clearly.
> Student Life Insurance Company wants to offer an insurance plan with a maximum claim amount of $5,000 for dorm students to cover theft of certain items. Past experience suggests that the probability of a maximum claim is .01. What premium should be charg
> There are five accounting exams. Bob’s typical score on each exam is a random variable with a mean of 80 and a standard deviation of 5. His final grade is based on the sum of his exam scores. (a) Find the mean and standard deviation of Bob’s point total
> The mean January temperature in Fort Collins, CO, is 37.18 F with a standard deviation of 10.38 F. Express these Fahrenheit parameters in degrees Celsius using the transformation C = 5y9F - 17.78.
> Pepsi and Mountain Dew products sponsored a contest giving away a Lamborghini sports car worth $215,000. The probability of winning from a single bottle purchase was .00000884. Find the expected value. Show your calculations clearly. (Data are from J. Pa
> The height of a Los Angeles Lakers basketball player averages 6 feet 7.6 inches (i.e., 79.6 inches) with a standard deviation of 3.24 inches. To convert from inches to centimeters, we multiply by 2.54. (a) In centimeters, what is the mean? (b) In centime
> In a certain Kentucky Fried Chicken franchise, half of the customer’s request “crispy” instead of “original,” on average. (a) What is the expected number of customers before the next customer requests “crispy”? (b) What is the probability of serving more
> In the Ardmore Hotel, 20 percent of the guests (the historical percentage) pay by American Express credit card. (a) What is the expected number of guests until the next one pays by American Express credit card? (b) What is the probability that the first
> Find each geometric probability. a. P(X = 5) when π = .50 b. P(X = 3) when π = .25 c. P(X = 4) when π = .60
> ABC Warehouse has eight refrigerators in stock. Two are side-by-side models and six are top freezer models. (a) Using Excel, calculate the entire hypergeometric probability distribution for the number of top-freezer models in a sample of four refrigerato
> 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.
> The probability that a passenger’s bag will be mishandled on a U.S. airline is .0046. During spring break, suppose that 500 students fly from Minnesota to various southern destinations. (a) What is the expected number of mishandled bags? (b) What is the
> In a string of 100 Christmas lights, there is a .01 chance that a given bulb will fail within the first year of use (if one bulb fails, it does not affect the others). Find the approximate probability that two or more bulbs will fail within the first yea
> The probability of a manufacturing defect in an aluminum beverage can is .00002. If 100,000 cans are produced, find the approximate probability of (a) at least one defective can and (b) two or more defective cans. (c) Is the Poisson approximation justifi
> An experienced order taker at the L.L. Bean call center has a .003 chance of error on each keystroke (i.e., π = .003). In 500 keystrokes, find the approximate probability of (a) at least two errors and (b) fewer than four errors. (c) Is the Poisson appro
> (a) Why might the number of yawns per minute by students in a warm classroom not be a Poisson event? (b) Give two additional examples of events per unit of time that might violate the assumptions of the Poisson model, and explain why.
> The average number of items (such as a drink or dessert) ordered by a Noodles & Company customer in addition to the meal is 1.4. These items are called add-ons. Define X to be the number of add-ons ordered by a randomly selected customer. (a) Justify the
> Calculate each compound event probability: a. P(X < 3), λ = 4.3 b. P(X > 7), λ = 5.2 c. P(X < 3), λ = 2.7
> Calculate each Poisson probability: a. P(X = 2), λ = 0.1 b. P(X = 1), λ = 2.2 c. P(X = 3), λ = 1.6
> Calculate each Poisson probability: a. P(X = 6), λ = 4.0 b. P(X = 10), λ = 12.0 c. P(X = 4), λ = 7.0
> Find the mean and standard deviation for each Poisson: a. λ = 9.0 b. λ = 12.0 c. λ = 7.0
> 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
> Find the mean and standard deviation for each Poisson: a. λ = 1.0 b. λ = 2.0 c. λ = 4.0
> Calculate each binomial probability: a. Fewer than 4 successes in 12 trials with a 10 percent chance of success. b. At least 3 successes in 7 trials with a 40 percent chance of success. c. At most 9 successes in 14 trials with a 60 percent chance of suc
> Calculate each binomial probability: a. More than 10 successes in 16 trials with an 80 percent chance of success. b. At least 4 successes in 8 trials with a 40 percent chance of success. c. No more than 2 successes in 6 trials with a 20 percent chance o
> Calculate each compound event probability: a. X < 10, n = 14, π = .95 b. X > 2, n = 5, π = .45 c. X < 1, n = 10, π = .15
> Calculate each compound event probability: a. X < 3, n = 8, π = .20 b. X > 7, n = 10, π = .50 c. X < 3, n = 6, π = .70
> Calculate each binomial probability: a. X = 2, n = 8, π = .10 b. X = 1, n = 10, π = .40 c. X = 3, n = 12, π = .70
> Calculate each binomial probability: a. X = 5, n = 9, π = .90 b. X = 0, n = 6, π = .20 c. X = 9, n = 9, π = .80
> Find the mean and standard deviation for each binomial random variable: a. n = 30, π = .90 b. n = 80, π = .70 c. n = 20, π = .80
> Find the mean and standard deviation for each binomial random variable: a. n = 8, π = .10 b. n = 10, π = .40 c. n = 12, π = .50
> Write the probability of each italicized event in symbols (e.g., P(X > 5). a. At least 7 correct answers on a 10-question quiz (X = number of correct answers). b. Fewer than 4 “phishing” e-mails out of 20 e-mails (X = number of phishing e-mails). c. At
> 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)
> List the X values that are included in each italicized event. a. You can miss at most 2 quizzes out of 16 quizzes (X = number of missed quizzes). b. You go to Starbuck’s at least 4 days a week (X = number of Starbuck’s visits). c. You are penalized if y
> 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
> Find the mean and standard deviation of four-digit uniformly distributed lottery numbers (0000 through 9999).
> Which of the following could not be probability distributions? Explain. Example A Example B Example C P(x) P(x) P(x) .80 1 .05 50 .30 1 .20 2 .15 60 .60 3 .25 70 .40 4 .40 5 .10
> “The probability of rolling three sevens in a row with dice is .0046.”
> “Commercial rocket launches have a 95% success rate.”
> “There is a 25% chance that AT&T Wireless and Verizon will merge.”
> Find the following combinations nCr: a. n = 8 and r = 3. b. n = 8 and r = 5. c. n = 8 and r = 1. d. n = 8 and r = 8.
> Find the following permutations nPr: a. n = 8 and r = 3. b. n = 8 and r = 5. c. n = 8 and r = 1. d. n = 8 and r = 8.
> (a) In how many ways could you arrange seven books on a shelf? (b) Would it be feasible to list the possible arrangements?
> 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 σ 5 $3.00. If 20 percent of all part time seasonal employees make more than $13.16 an hour, what is
> Bob has to study for four final exams: accounting (A), biology (B), communications (C), and drama (D). (a) If he studies one subject at a time, in how many different ways could he arrange them? (b) List the possible arrangements in the sample space.
