Question:

> 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.

> Until 2005, the UPC bar code had 12 digits (0–9). The first six digits represent the manufacturer, the next five represent the product, and the last is a check digit. (a) How many different manufacturers could be encoded? (b) How many different products

> American Express Business Travel uses a six-letter record locator number (RLN) for each client’s trip (e.g., KEZLFS). (a) How many different RLNs can be created using capital letters (A–Z)? (b) What if they allow any mixture of capital letters (A–Z) and

> (a) Find 20C5 without a calculator. Show your work. (b) Use your calculator to find 20C5. (c) Find 20C5 by entering “20 choose 5” in the Google search window. (d) Which method would you use most often? Why?

> (a) Find 8! without a calculator. Show your work. (b) Use your calculator to find 32!. (c) Find 32! by typing “32!” in the Google search window. (d) Which method would you use most often? Why?

> Half of a set of the parts are manufactured by machine A and half by machine B. Four percent of all the parts are defective. Six percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A,

> A study showed that 60 percent of The Wall Street Journal subscribers watch CNBC every day. Of these, 70 percent watch it outside the home. Only 20 percent of those who don’t watch CNBC every day watch it outside the home. Let D be the event “watches CNB

> Of grocery shoppers who have a shopping cart, 70 percent pay by credit/debit card (event C1), 20 percent pay cash (event C2), and 10 percent pay by check (event C3). Of shoppers without a grocery cart, 50 percent pay by credit/debit card (event C1), 40 p

> A die is thrown (1, 2, 3, 4, 5, 6) and a coin is tossed (H, T). (a) Enumerate the elementary events in the sample space for the die/coin combination. (b) Are the elementary events equally likely? Explain.

> For a continuous PDF, why can’t we sum the probabilities of all x-values to get the total area under the curve?

> At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .38. Use Excel to find the probability that in a sample of 5 customers (a) none of the 5 will order a nonalcoholic beverage, (b) at least 2 will, (c)

> Based on the previous problem, is major independent of gender? Explain the basis for your conclusion.

> The contingency table below summarizes a survey of 1,000 bottled beverage consumers. Find the following probabilities or percentages: a. Probability that a consumer recycles beverage bottles. b. Probability that a consumer who lives in a state with a de

> Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 80 percent order a soft drink, and 40 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? Explain.

> A hospital’s backup power system has three independent emergency electrical generators, each with uptime averaging 95 percent (some downtime is necessary for maintenance). Any of the generators can handle the hospital’s power needs. Does the overall reli

> A baseball player bats either left-handed (L) or right-handed (R). The player either gets on base (B) or does not get on base (B9). (a) Enumerate the elementary events in the sample space. (b) Would these elementary events be equally likely? Explain.

> The probability that a student has a Visa card (event V) is .73. The probability that a student has a MasterCard (event M) is .18. The probability that a student has both cards is .03. (a) Find the probability that a student has either a Visa card or a M

> Given P(A) = .40, P(B) = .50, and P(A ∩ B) = .05. (a) Find P(A | B). (b) In this problem, are A and B independent?

> Given P(A) = .40, P(B) = .50. If A and B are independent, find P(A ∩ B).

> Given P(J) = .26, P(K) = .48. If A and B are independent, find P(J ∪ K).

> List more than two events (i.e., categorical events) that might describe the outcome of each situation. a. A student applies for admission to Oxnard University. b. A football quarterback throws a pass. c. A bank customer makes an ATM transaction.

> 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

> A survey asked tax accounting firms their business form (S 5 sole proprietorship, P 5 partnership, C 5 corporation) and type of risk insurance they carry (L 5 liability only, T 5 property loss only, B 5 both liability and property). (a) Enumerate the ele

> List two mutually exclusive events that describe the possible outcomes of each situation. a. A pharmaceutical firm seeks FDA approval for a new drug. b. A baseball batter goes to bat. c. A woman has a mammogram test.

> Suppose the probability of an IRS audit is 1.7 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more. (a) What are the odds that such a taxpayer will be audited? (b) What are the odds against such a taxpayer being audited?

> Suppose Samsung ships 21.7 percent of the liquid crystal displays (LCDs) in the world. Let S be the event that a randomly selected LCD was made by Samsung. Find (a) P(S), (b) P(S’), (c) the odds in favor of event S, and (d) the odds against event S.

> Given P(A) = .70, P(B) = .30, and P(A ∩ B) = .00, find (a) P(A ∪ B), (b) P(A | B), and (c) P(B | A).

> Given P(A) = .40, P(B) = .50, and P(A ∩ B) = .05, find (a) P(A ∪ B), (b) P(A | B), and (c) P(B | A).

> An entrepreneur who plans to open a Cuban restaurant in Nashville has a 20 percent chance of success.

> Based on the reported experience of climbers from a given year, a climber who attempts Everest has a 31 percent chance of success.

> A credit card customer at Barnes and Noble can use Visa (V), MasterCard (M), or American Express (A). The merchandise may be books (B), electronic media (E), or other (O). (a) Enumerate the elementary events in the sample space describing a customer’s pu

> An exam has a mean of 70 with a standard deviation of 10. Use Chebyshev’s Theorem to find a lower bound for the number of students in a class of 400 who scored between 50 and 90.

> 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

> (a) By Chebyshev’s Theorem, at least how many students in a class of 200 would score within the range μ 6 2σ? (b) By the Empirical Rule, how many students in a class of 200 would score within the range μ 6 2σ? (c) What assumption is required in order to

> Noodles and Company tested consumer reaction to two spaghetti sauces. Each of 70 raters assessed both sauces on a scale of 1 (worst) to 10 (best) using several taste criteria. To correct for possible bias in tasting order, half the raters tasted Sauce A

> Use Excel’s AVEDEV function to find the mean absolute deviation (MAD) of these five numbers: 12, 18, 21, 22, 27.

> Use Excel’s AVEDEV function to find the mean absolute deviation (MAD) of the integers 1 through 10.

> Over the past month, Bob’s bowling score mean was 182 with a standard deviation of 9.1. His bowling partner Cedric’s mean was 152 with a standard deviation of 7.6. Which bowler is more consistent in relative terms?

> (a) Make a scatter plot of the following data on X 5 home size and Y 5 selling price (thousands of dollars) for new homes (n 5 20) in a suburb of an eastern city. (b) Find the sample correlation coefficient. (c) Is there a linear relationship between X a

> In fuel economy tests in city driving conditions, a hybrid vehicle’s mean was 43.2 mpg with a standard deviation of 2.2 mpg. A comparably sized gasoline vehicle’s mean was 27.2 mpg with a standard deviation of 1.9 mpg. Which vehicle’s mpg was more consis

> Your laptop gets warm (even hot) when you place it on your lap because it is dissipating heat from its microprocessor and related components. (a) Use the information in the following table to make a scatter plot. (b) Describe the relationship between Mic

> The number of Internet users in Latin America grew from 78.5 million in 2000 to 156.6 million in 2010. Use the geometric mean to find the annual growth rate.

> An executive&acirc;&#128;&#153;s telephone log showed the lengths of 65 calls initiated during the last week of July. (a) Find the mean, median, mode, midrange, geometric mean, and 10 percent trimmed mean. (b) Are the data symmetric or skewed? If skewed,

> 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.

> On Friday night, the owner of Chez Pierre in downtown Chicago noted the amount spent for dinner at 28 four-person tables. (a) Find the mean, midrange, geometric mean, and 10 percent trimmed mean. (b) Do these measures of center agree? Explain. 95 10

> On San Martin Boulevard, embedded sensors kept track of the vehicle traffic count each hour for five weekdays, Monday through Friday between 6 a.m. and 8 p.m. (5 weeks 3 14 hours 5 70 observations). (a) Visually estimate the quartiles Q1, Q2, Q3. (b) Est

> CitiBank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays. (a) Find the mean, midrange, geometric mean, and 10 percent trimmed mean. (b) Do these measures of center agree? Explain. 25 37 23 26 30

> Coffee temperatures (degrees Fahrenheit) at a certain restaurant have quartiles Q1 = 160, Q2 = 165, and Q3 = 170. Using the inner fences as a criterion, would a temperature of 149 be considered an outlier?

> Waiting times (minutes) for a table at Joey’s BBQ on Friday at 5:30 p.m. have quartiles Q1 = 21, Q2 = 27 and Q3 = 33. Using the inner fences as a criterion, would a wait time of 45 minutes be considered an outlier?

> In 2007, total compensation (in thousands of dollars) for 40 randomly chosen CEOs ranged from 790 to 192,920, with quartiles Q1 = 3,825, Q2 = 8,890, and Q3 = 17,948. (a) Sketch a simple boxplot (5-number summary without fences) using a nicely scaled X-ax

> Scores on an accounting exam ranged from 42 to 96, with quartiles Q1 = 61, Q2 = 77, and Q3 = 85. (a) Sketch a simple boxplot (5-number summary without fences) using a nicely scaled X-axis. (b) Describe its shape (skewed left, symmetric, skewed right).

> (a) Write the Excel function for the 10 percent trimmed mean of a data set in cells A1:A50. (b) How many observations would be trimmed in each tail? (c) How many would be trimmed overall?

> An executive&acirc;&#128;&#153;s telephone log showed the lengths of 65 calls initiated during the last week of July. (a) Sort the data. (b) Find the mean, median, and mode. (c) Do the measures of center agree? Explain. (d) Are the data symmetric or skew