Midterm Practice Questions
There is a 70 percent chance that an airline passenger will check bags. In the next 16 passengers that check in for their flight at Denver International Airport. (a) Find the probability that all will check bags. (Round your answer to 4 decimal places.) P(X = 16) (b) Find the probability that fewer than 10 will check bags. (Round your answer to 4 decimal places.) P(X < 10) (c) Find the probability that at least 10 will check bags. (Round your answer to 4 decimal places.) P(X ≥ 10)
(a) Excel: = BINOM.DIST(16,16,.7,0). = .0033 (b) P(X < 10) = P(X ≤ 9) = BINOM.DIST(9,16,.7,1) = .1753. (c) P(X ≥ 10) = 1 − P(X ≤ 9) = 1 − BINOM.DIST(9,16,.7,1) = .8247.
Consider the following probability histogram for a discrete random variable X: Value of X 1 2 3 4 5 Probability 0.10 0.25 0.30 0.20 0.15 What is P(X ≤ 3)?
0.65
Based on past data, the probability that a customer at a certain Noodles & Company restaurant will order a dessert (event D) with the meal is .08. The probability that a customer will order a bottled beverage (event B) is .14. The joint probability that a customer will order both a dessert and a bottled beverage is .0112. Is ordering a dessert independent of ordering a bottled beverage?
Yes, ordering a dessert is independent of ordering a bottled beverage .08*.14 = .0112
Calculate each binomial probability: (a) X = 2, n = 8, π= .10 (Round your answer to 4 decimal places.) P(X = 2) = ? (b) X = 1, n = 10, π= .40 (Round your answer to 4 decimal places.) P(X = 1) = ? (c) X = 3, n = 12, π= .70 (Round your answer to 4 decimal places.) P(X = 3) = ?
a) =BINOM.S(2,8,.10,FALSE) = .1488 b) =BINOM.S(1,10,.40,FALSE) = .0403 c) =BINOM.S(3,12,.70,FALSE) = .0015
Which survey questions below would be suitable for a set of check boxes providing choices for the respondent to choose from? (Select all that apply) a) How concerned are you for the environment? b) What company do you work for? c) What is your salary range? d) What was the amount of your last utility bill?
a) How concerned are you for the environment? c) What is your salary range?
A die is thrown (1, 2, 3, 4, 5, 6) and a coin is tossed (H, T). (a) Choose the sample space for the die/coin combination for the elementary events given. S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)} S = {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)} S = {(H,H), (H,T), (T,H), (T,T)} S = {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)} (b) Are the elementary events equally likely? - Yes - No
a) S = {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)} b) Yes, assuming that we have a fair die and fair coin.
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) Choose the correct sample space from the given elementary events. S = {(V,B), (V,E), (V,O), (M,B), (M,E), (M,O), (A,B), (A,E), (A,O)} S = {(V,B), (V,E), (V,O), (B,B), (A,E), (A,O)} S = {(A,B), (V,E), (A,O), (M,B), (M,E), (M,O)} S = {(O,B), (A,E), (V,O), (V,B), (M,E), (M,O), (M,B), (A,E)} Would each elementary event be equally likely? - No, not equally likely. - Yes, equally likely.
a) S = {(V,B), (V,E), (V,O), (M,B), (M,E), (M,O), (A,B), (A,E), (A,O)} (b) Events are not equally likely. Barnes and Noble probably carries more books than other merchandise.
What type of data (categorical, discrete numerical, or continuous numerical) is each of the following variables? (a) The manufacturer of your car. (b) Your college major. (c) The number of college credits you are taking.
a) categorical b) categorical c) discrete numerical
Would you use a sample or census to measure each of the following? (a) The number of workers currently employed by Campbell Soup Company. (b) The average price of a can of Campbell's Cream of Mushroom soup. (c) The total earnings of workers employed by Campbell Soup Company last year.
a) census b) sample c) census
What type of data (categorical, discrete numerical, or continuous numerical) is each of the following variables? (a) The miles on your car's odometer. (b) The fat grams you ate for lunch yesterday. (c) The name of the airline with the cheapest fare from New York to London. (d) The brand of cell phone you own.
a) continuous numerical b) continuous numerical c) categorical d) categorical
You want to find out what people felt to be the most important problem facing society today. What is better: a. to give a fixed set of choices from which they must choose b. to give an open-ended question that allowed them to specify whatever they wished
a) to give a fixed set of choices from which they must choose
How can you tell when the point has been reached where you should call for an expert statistician? a) when you've reached the limit of your statistical expertise b) when your boss asks for a report of last week's sales data and you had planned to leave work early c) when you're looking for a promotion
a) when you've reached the limit of your statistical expertise
Which of the two displays (table or graph) is more helpful in visualizing the relationship between restaurant size and interior seating for 74 Noodles restaurants? a) The graph and table are mutually exclusive in use. b) The graph is much more useful. c) The table is much more useful. d) Neither are useful.
b) The graph is much more useful.
How much statistics does a business student need to know? (select all that apply) a) not much --- consultants do most of the statistical analysis b) enough to handle everyday data problems c) enough to feel confident discussing a colleague's data analysis d) enough to know when to call a statistical expert
b) enough to handle everyday data problems c) enough to feel confident discussing a colleague's data analysis d) enough to know when to call a statistical expert
A financial magazine publishes an annual list of major stock funds. Last year, the list contained 1,699 funds. What method would you recommend to obtain a sample of 20 stock funds? a) judgement sampling b) simple random sample or systematic sampling c) cluster sampling or convenience sampling
b) simple random sample or systematic sampling
Are the private polls and surveys more trustworthy than government statistics? (according to the ted talk)
yes
Based on past data, the probability that a customer at a certain Noodles & Company restaurant will order a dessert (event D) with the meal is .08. The probability that a customer will order a bottled beverage (event B) is .14. The joint probability that a customer will order both a dessert and a bottled beverage is .0112. Is ordering a dessert independent of ordering a bottled beverage? yes, independent no, not independent
yes, they're independent of each other
Are Levi's 501 jeans really "in" on campus? Based on the list of clothing choices used for the survey, is it a valid conclusion?
No
What was measured to access the danger posed by the cereal?
glyphosate (herbicide found in weed-killing poison that is linked to cancer)
The U.S. Fisheries and Wildlife Service requires that scallops harvested from the ocean must weigh at least 1/36 pound. The harbormaster at a Massachusetts port randomly selected 18 bags of scallops from 11,000 bags on an arriving vessel. The average scallop weight from the 18 bags was 1/39 pound. (a) Would the population of 11,000 bags be considered effectively infinite in this case? (b) Which value represents a sample statistic: 1/36 or 1/39?
a) yes b) 1/139
Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?" Here is the distribution of responses, combining many separate languages from the broad Asian/Pacific region (from Statistics Canada, www.statcan.ca): Language English French Asian/Pacific Other Probability ? 0.23 0.07 0.11 What probability should replace "?" in the distribution?
0.59
Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 10 percent are returned. If eight rings are sold today, what is the probability that fewer than three will be returned? a) .9950 b) .9619 c) .0331 d) .1488
b) .9619
Ephemeral Services Corporation (ESCO) knows that nine other companies besides ESCO are bidding for a $900,000 government contract. Each company has an equal chance of being awarded the contract. If ESCO has already spent $100,000 in developing its bidding proposal, what is its expected net profit? a) $100,000 b) $90,000 c) -$10,000 d) $0
c) -$10,000
Suppose you had a telephone directory listing all the businesses in a city, alphabetized by type of business. If you wanted to phone 100 of them to get a representative sampling of opinion on some issue. You need to select which 100 to phone. Would it be a good idea to simply use the first 100 businesses listed?
no
was the cereal and oat research that we learned about an observational study or research study?
observational study
How can you spot a bad statistics (according to the ted talk) ?
question 1: can you see uncertainty? question 2: can I see myself in the data? question 3: how was the data collected
On Friday night, the owner of Chez Pierre in downtown Chicago noted the amount spent for dinner at 28 four-person tables. Below is a sample of the amounts spent: 103, 109, 170, 114, 113, 107 Find the median amount spent for a dinner. Report the numerical answer only. Do not include $ sign in your answer.
111
On average, 20% of the emergency room patients at Greenwood General Hospital lack health insurance. Assume 4 random patients arrive to ER. a) What is the probability that at least 2 will be uninsured? Report your answer as a percentage (do not include the % symbol) Hint: Use =BINOM.DIST.RANGE()
18.08
The mean collection period for accounts receivable at Ephemeral Products is 18.5 days with a standard deviation of 4.8 days. What is the standardized z-score for an account that is paid in 30 days? (Round your answer to 3 decimal places.)
2.396
On Friday night, the owner of Chez Pierre in downtown Chicago noted the amount spent for dinner at 28 four-person tables. Below is a sample of the amounts spent: 103, 109, 170, 114, 113, 107 Find the standard deviation of the amount spent for a dinner. Round your answer to cents. Report only the numerical value, no special symbols like $.
25.14
It is important to a small quick oil change shop to ensure that a car's service time is not considered "late" by the customer. Service times are defined as either late or not late. Based on past records, 10% of the cars were late. Assumptions: - cars are independent of each other - probability of a late car is consistent Assume that on average the shop services 12 cars per shift. What are the chances that all 12 cars will be serviced on time? Report your answer as a percentage (without the % symbol), round to two decimals.
28.24
The mean collection period for accounts receivable at Ephemeral Products is 18.5 days with a standard deviation of 4.8 days. How many days (to the nearest integer) would qualify an account as an outlier?
33
Calculate the data value that corresponds to the following z-score: weekly grocery bill: James' z-score = -1.45, mean = $53, standard deviation = $12.
35.6
On average, 20% of the emergency room patients at Greenwood General Hospital lack health insurance. Assume 4 random patients arrive to ER. Based on the past records an uninsured patient on average costs the ER about $600.00. How much is the Greenwood General Hospital ER is expected to loose on a random 4 patients? Download "ER_case.xlsx" file and use it for your calculations.
480.0
An simple random sample of 1200 adult Americans was selected and asked: "In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?" Thirty-nine percent of those responding answered yes. What type of bias if any has occurred? a) no bias b) response bias c) non-response bias d) under coverage bias e) wording bias
e) wording bias
A real estate website reported that the median price of single family homes sold in the past 9 months in the local area was $136,900 and the average price was $161,447. Which do you think is more useful to someone considering the purchase of a home, the median or the average?
median
In a study of standard of living of typical families in Middletown, a sociologist makes a numerical summary of family income in that city. What should she use? median or average?
median
Ann Landers asked whether they though engineers make good husbands. Do you think the responses she got are representative of public opinion?
no
Recent study shows SAT and ACT scores are approximately normally distributed. The mean SAT scores is 1026, and standard deviation is 209. For ACT, the mean is 20.8 and the standard deviation is 4.8. Tanya scored 1318 on SAT and Jeremiah scored 26 ACT. Who did better?
tanya
Why do you think there is less trust in the government statistics? (ted talk)
the government might skew numbers towards their favor to prevent any scandals
how do you know if a distribution is skewed to the right?
when the mean is larger than the median and mode.
Middletown is considering imposing an income tax on citizens. City hall wants a numerical summary of its citizens' income to estimate the total tax base. What should they use? median or average?
average
It is important to a small quick oil change shop to ensure that a car's service time is not considered "late" by the customer. Service times are defined as either late or not late. Based on past records, 10% of the cars were late. Assumptions: - cars are independent of each other - probability of a late car is consistent Assume that on average the shop services 12 cars per shift. What is the variability of the expected number of "late" services? Round you answer to two decimals.
1.04
Two cards are selected at random and the denomination is recorded. The event H is defined as the event that the first card is hearts. Which of the following correctly defines event H?
H = {(hearts, diamonds), (hearts, clubs), (hearts, spades), (hearts, hearts)}
Who performed the study the newspaper article is based on?
EWG (environmental working group)
Your manager feel that it is unfair to have half of the employees stay with the old bonus structure. You need to convince her that using last quarter records for the reference is not a good idea. Report at least one confounding factor that can be present in case the historic data are used.
If the old bonus structure is wiped out completely, there won't be an accurate comparison for the new structure to be measured by.
Given P(A) = 0.40, P(B) = 0.50. If A and B are independent, find P(A ∩ B). P(A ∩ B) = ?
P(A∩B) = P(A) × P(B) = 0.40 × 0.50 = 0.2000.
A standard deck of cards has 52 cards. The cards have one of 2 colors: 26 cards in the deck are red and 26 are black. The cards have one of 4 denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). Two cards are selected at random and the color is recorded. Which of the following is the correct sample space S for the set of possible outcomes?
S = {(red, red), (red, black), (black, red), (black, black)}
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?
YES: Ordering a soft drink is independent of ordering a square pizza. P(ordering a soft drink) × P(ordering a square pizza) = .5(.8) = .4. This is equal to P(ordering both a soft drink and a square pizza).
Newsletter distributed by politician to his constituents gave results of nationwide survey on Americans' attitudes about educational issues. One question: "Should your legislature adopt a policy to assist children in failing schools to opt out of that school and attend an alternative school—public, private, or parochial—of the parents' choosing?" From wording of question, can you speculate on what answer was desired? a) yes, they should b) no, they should not
a) yes, they should
For each data set, which best indicates a "typical" data value (mean, median, either)? a. Days on campus by 11 students: 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5 b. P/E ratios of 6 stocks: 1.5, 6.5, 6.6, 7.3, 8.2, 9.1 c. Textbooks in 9 backpacks: 0, 0, 0, 0, 0, 1, 2, 3, 4
a. Either of the measures would work because the data set is symmetrical. Mean = Median = 3 b. The median is a better choice because the data set is slightly skewed left. Mean = 6.53 and median = 6.95. c. The median is a better choice than the mean because the data is skewed right. Mean = 1.11 and median = 0.
For each data set, find the mean, median, and mode. (a) Campus health center visits (12 students): 0, 0, 0, 0, 0, 1, 2, 3, 3, 5, 5, 15 (Round your answers to 2 decimal places.) (b) Red Rocks ticket prices (9 concerts): 40, 40, 65, 71, 72, 75, 76, 78, 98 (Round your answers to 2 decimal places.) (c) Sodium grams in canned soup (8 varieties): 225, 255, 295, 302, 304, 337, 351, 366 (Round your answers to 2 decimal places.)
(a) Mean = 2.83, Median = 1.5, Mode = 0 (b) Mean = 68.33, Median = 72, Mode = 40 (c) Mean = 304.38, Median = 303, No mode.
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 MasterCard. (Round your answer to 2 decimal places.) (b) In this problem, are V and M independent?
(a) P(V ∪ M) = P(V) + P(M) - P(V ∩ M) = .73 + .18 - .03 = .88. (b) P(V ∩ M) ≠ P(V) × P(M) therefore V and M are not independent.
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 Starbucks at least 4 days a week (X = number of Starbucks visits). (c) You are penalized if you have more than 3 absences out of 10 lectures (X = number of absences).
(a) X = 0, 1, or 2 (b) X = 4, 5, 6, or 7 (c) X = 4, 5, 6, 7, 8, 9, or 10
The mean monthly rent of students at Oxnard University is $875 with a standard deviation of $219. (a) John's rent is $1,325. What is his standardized z-score? (Round your answer to 3 decimal places.) (b) Is John's rent an outlier? (c) How high would the rent have to be to qualify as an outlier?
(a) z = (1325 − 875)/219 = 2.055. (b) Because John's standardized score is greater than 2 but less than 3 we would consider his rent unusual but not an outlier. (c) John's rent would be considered an outlier if John's z score > 3. Set z = rent−875 / 219 and solve for rent. Rent = $1,532
The mean collection period for accounts receivable at Ephemeral Products is 18.5 days with a standard deviation of 4.8 days. (a) What is the standardized z-score for an account that is paid in 30 days? (Round your answer to 3 decimal places.) (b) Is that account an outlier? (c) How many days (to the nearest integer) would qualify an account as an outlier?
(a) z = (30 − 18.5)/4.8 = 2.396. (b) Because the account's standardized score is greater than 2 but less than 3 we would consider his rent unusual but not necessarily an outlier. (c) An account would be considered an outlier if z score > 3. Set z = 3 = days - 18.5 / 4.8 and solve for days. Days = 32.9
Identify the following data as either time series or cross-sectional. (a) The 2017 CEO compensation of the 500 largest U.S. companies. (b) The annual compensation for the CEO of Coca-Cola Enterprises from 2010 to 2017. (c) The weekly revenue for a Noodles & Company restaurant for the 52 weeks in 2017. (d) The number of skiers on the mountain on Christmas Day 2017 at each of the ski mountains owned by Vail Resorts.
(a) Cross-sectional. A single point in time: end of 2017. (b) Time series. Data are collected over an 8-year time period. (c) Time series. Data collected over 52 weeks. (d) Cross-sectional. Single point in time: Christmas Day 2017
Police records in the town of Saratoga show that 15 percent of the drivers stopped for speeding have invalid licenses. If 12 drivers are stopped for speeding. (a) Find the probability that none will have an invalid license. (Round your answer to 4 decimal places.) (b) Find the probability that exactly one will have an invalid license. (Round your answer to 4 decimal places.) (c) Find the probability that at least 2 will have invalid licenses. (Round your answer to 4 decimal places.)
(a) P(X = 0) = BINOM.DIST(0,12,.15,0). = .1422 (b) P(X = 1) = BINOM.DIST(1,12,.15,0). = .3012 (c) P(X ≥ 2) = 1 − P(X ≤ 1) = 1 − BINOM.DIST(1,12,.15,1) = .5565.
Calculate each binomial probability: (a) Fewer than 4 successes in 12 trials with a 10 percent chance of success. (Round your answer to 4 decimal places.) (b) At least 3 successes in 7 trials with a 40 percent chance of success. (Round your answer to 4 decimal places.) (c) At most 9 successes in 14 trials with a 60 percent chance of success. (Round your answer to 4 decimal places.)
(a) Use the Excel function = BINOM.DIST(x,n,π,1) where "1" stands for cumulative. P(X < 4 ) = P(X ≤ 3) = BINOM.DIST(3,12,.10,1) = .9744. (b) P(X ≥ 3) = 1 - P(X ≤ 2) = 1 - BINOM.DIST(2,7,.40,1) = .5801. (c) P(X ≤ 9) = BINOM.DIST(9,14,.60,1) = .7207.
Consider the following probability histogram for a discrete random variable X: Value of X 1 2 3 4 5 Probability 0.10 0.25 0.30 0.20 0.15 What is the P(X = 3)?
0.3
Consider the following probability histogram for a discrete random variable X: Value of X 1 2 3 4 5 Probability 0.10 0.25 0.30 0.20 0.15 What is the P(X < 3)?
0.35
Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?" Here is the distribution of responses, combining many separate languages from the broad Asian/Pacific region (from Statistics Canada, www.statcan.ca): Language English French Asian/Pacific Other Probability ? 0.23 0.07 0.11 What is the probability that a Canadian's mother tongue is not English?
0.41
Suppose a website has 2 independent file servers. Each server has 99% reliability. What is the total system reliability (the probability that one or both servers is "up")?
0.9999
Suppose a website has 2 independent file servers. Each server has 99% reliability. What is the chance that both servers are down. Report your answer as a proportion.
0.0001
On average, 20% of the emergency room patients at Greenwood General Hospital lack health insurance. Assume 4 random patients arrive to ER. What is the probability that all 4 will be uninsured? Report your answer as a percentage (do not include the % symbol)
0.16
It is important to a small quick oil change shop to ensure that a car's service time is not considered "late" by the customer. Service times are defined as either late or not late. Based on past records, 10% of the cars were late. Assumptions: - cars are independent of each other - probability of a late car is consistent Assume that on average the shop services 12 cars per shift. How many customers are expected to receive "late" service?
1.2
A company is working on a new bonus structure that is designed to improve employee satisfaction, productivity, and motivation. After long hours the program is ready. Now you need convince your upper management that the new bonus system is more effective than the current one. To do that you need to collect data. There are several ways you can do it. Consider the options below. Choose the one that would give you the most accurate evaluation of the new program. a. Start using the new bonus system during the upcoming quarter and check whether employees are happy with it. Use that data to report new program performance. b. Use both bonus systems during the upcoming quarter. Randomly assign half of the employees to receive bonus according to the current system and half - according to the new bonus structure. Compare the employee satisfaction in two groups at the end of the quarter. c. Use the new bonus system during the upcoming quarter and compare the employee satisfaction with the numbers from last quarter when the old system was used.
B) Use both bonus systems during the upcoming quarter. Randomly assign half of the employees to receive bonus according to the current system and half - according to the new bonus structure. Compare the employee satisfaction in two groups at the end of the quarter.
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 of no loss is .40. Find the expected loss. (Input the amount as a positive value.)
Let X equal the loss during a hurricane. The values of X are either $250 million, $950 million, or $0. Expected Loss = E(X ) = $250(.3) + $950(.3) + $0(.4) = $360 million.
Recently, researchers estimated that 76.8 percent of global e-mail traffic was spam. Could a census be used to update this estimate?
No, a census would be too difficult since this is an infinite population (people can continue to send e-mails).
Given P(A) = 0.40, P(B) = 0.50. If A and B are independent, find P(A ∩ B).
P(A∩B) = P(A) × P(B) = 0.40 × 0.50 = 0.2000.
Historically, 5 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database. The number of customers out of 12 who have an incorrect address in the database is a binomial random variable with n = 12 and π = .05. (a) What is the probability that none of the next 12 repeat customers who call will have an incorrect address? (Round your answer to 4 decimal places.) (b) What is the probability that one customer who calls will have an incorrect address? (Round your answer to 4 decimal places.) (c) What is the probability that two customers who call will have an incorrect address? (Round your answer to 4 decimal places.) (d) What is the probability that fewer than three customers who call will have an incorrect address? (Round your answer to 4 decimal places.)
The number of customers out of 12 who have an incorrect address in the database is a binomial random variable with n = 12 and π = .05. a) Excel: = BINOM.DIST(0,12,.05,0). = .5404 b) Excel: = BINOM.DIST(1,12,.05,0). = .3413 c) Excel: = BINOM.DIST(2,12,.05,0). = .0988 d) Excel: = BINOM.DIST(2,12,.05,1) = .9804
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .38. a. Find the probability that in a sample of 5 customers, none of the 5 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) b. Find the probability that in a sample of 5 customers, at least 2 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) c. Find the probability that in a sample of 5 customers, fewer than 4 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) d. Find the probability that in a sample of 5 customers, all 5 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.)
The number of customers out of the next 5 who order a nonalcoholic beverage is a binomial random variable with n = 5 and π = .38. a. P(X = 0) = BINOM.DIST(0,5,.38,0) = .0916 b. P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - BINOM.DIST(1,5,.38,1) = .6276 c. P(X < 4) = P(X ≤ 3) = BINOM.DIST(3,5,.38,1) = .9274 d. P(X = 5) = BINOM.DIST(5,5,.38,0) = .0079
how do you find the proportion of a table/population?
divide the wanted sample/ total sample
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. (Round your answer to 4 decimal places.)
X is the amount of the "value" of a bottle. X can be either $215,000, the value of the Lamborghini, or $0. To find the expected value multiply each value of X by the associated probability. E(X) = ($215,000)(.00000884) + ($0)(.99999116) = 1.9006.
A die is rolled. If it rolls to a 1, 2, or 3, you win $2. If it rolls to a 4, 5, or 6, you lose $1. Calculate the expected winnings. a) $0.50 b) $3.00 c) $1.50 d) $1.00
a) $0.50
List some benefits that would govern the decision to call an expert statistician. (Select all that apply) a) Better sampling strategies, which can result in more useful data. b) Better understanding of what information can be extracted from the data. c) Greater confidence in the results. d) Projects are always delivered on time.
a) Better sampling strategies, which can result in more useful data. b) Better understanding of what information can be extracted from the data. c) Greater confidence in the results.
Which pairs of events are independent? (a) P(A) = 0.60, P(B) = 0.40, P(A ∩ B) = 0.24. A and B are ? (b) P(A) = 0.90, P(B) = 0.20, P(A ∩ B) = 0.18. A and B are ? (c) P(A) = 0.50, P(B) = 0.70, P(A ∩ B) = 0.25. A and B are ?
a) P(A) × P(B) = 0.40 × 0.60 = 0.24 and P(A ∩ B) = 0.24; therefore, A and B are independent. b) P(A) × P(B) = 0.90 × 0.20 = 0.18 and P(A ∩ B) = 0.18; therefore, A and B are independent. c) P(A) × P(B) = 0.50 × 0.70 = 0.35 and P(A ∩ B) = 0.25; therefore, A and B are not independent.
Given P(A) = .40, P(B) = .50, and P(A ∩ B) = .05: (a) Find P(A U B). (Round your answer to 2 decimal places.) (b) Find P(A | B). (Round your answer to 2 decimal places.) (c) Find P(B | A). (Round your answer to 3 decimal places.)
a) P(A∪B) = P(A)+P(B) − P(A∩B) = .4+.5−.05n = .85 b) P(A|B) = P(A∩B)/P(B) =. 05/.50 = .10 c) P(B|A) = P(A∩B)/P(A) = .05/.4 = .125
Let C be the event that a randomly chosen adult has some college education. Let M be the event that a randomly chosen adult is married. Given P(C) = .4, P(M) = .5 and P(C ∩ M) = .24, find each probability. a) Find P(C′). (Round your answer to 1 decimal place.) b) Find P(C ∪ M). (Round your answer to 2 decimal places.) c) Find P(M | C). (Round your answer to 1 decimal place.) d) Find P(C | M). (Round your answer to 2 decimal places.)
a) P(C') = 1−P(C) = 1−.4 = .6 b) P(C∪M) = P(C)+P(M)−P(C∩M) = .4+.5−.24=.66 c) P(M|C) = P(C∩M)/P(C) = .24/.4 = .6 d) P(C|M) = P(C∩M)/P(M) = .24/.5 = .48
Which type of data (cross-sectional or time series) is each variable? (a) Scores of 50 students on a midterm accounting exam last semester. (b) Bob's scores on 10 weekly accounting quizzes last semester. (c) Average score by all takers of the state's CPA exam for each of the last 10 years. (d) Number of years of accounting work experience for each of the 15 partners in a CPA firm.
a) cross-sectional b) time series c) time series d) cross-sectional
Jason is buying a new computer. He is comparing various models using many different variables. These variables play an important role in making the decision about which computer he will buy. Identify which of the following variables is/are categorical. a) does the computer come with a CD/DVD writer? b) what is the memory capacity of the computer? c) is the computer a laptop or desktop model? d) how much does the computer cost?
a) does the computer come with a CD/DVD writer? c) is the computer a laptop or desktop model?
A researcher found that out of 500 searches on major search engines for the keyword phrase "ring tone," more than 40 percent were fake pages created by spammers. (a) What kind of probability is this? - classical - subjective - empirical (b) How would it have been derived? - Based on the personal judgment about the likelihood of an event - Results from a study - Without actually doing a search
a) empirical b) results from a study
An entrepreneur who plans to open a Cuban restaurant in Nashville has a 20 percent chance of success. Which kind of probability is it? (Select all that apply) a) Empirical b) Classical c) Subjective
a) empirical c) subjective
Find the mean and standard deviation for each binomial random variable: a. n = 30, π = .90 (Round your standard deviation to 4 decimal places.) b. n = 80, π = .70 (Round your standard deviation to 4 decimal places.) c. n = 20, π= .80 (Round your standard deviation to 4 decimal places.)
a) mean = nπ = 30*.90 = 27 standard deviation = square root(n*π(1-π)) = square root(30*.90(1-.90) = 1.6432 b) mean = nπ = 80*.70 = 56 standard deviation = square root(n*π(1-π)) = square root(80*.70(1-.70) = 4.0988 c) mean = nπ = 20*.80 = 16 standard deviation = square root(n*π(1-π)) = square root(20*.80(1-.80) = 1.7789
You and a friend are each doing a survey to see if there is a relationship between height and happiness. Without discussing in advance, you both attempt to measure the height and happiness of the same 100 people. Are you more likely to agree on a) measurement of height b) measurement of happiness
a) measurement of height
The target population is all stocks in the S&P 500 index. Is each of the following a parameter or a statistic? (a) The average price/earnings ratio for all 500 stocks in the S&P index. (b) The proportion of all stocks in the S&P 500 index that had negative earnings last year. (c) The proportion of energy-related stocks in a random sample of 50 stocks. (d) The average rate of return for 20 stocks recommended by a broker.
a) parameter b) parameter c) statistic d) statistic
Would you expect Starbucks to use a sample or census to measure each of the following? (a) The percentage of repeat customers at a certain Starbucks on Saturday mornings. (b) The number of chai tea latte orders last Saturday at a certain Starbucks. (c) The average temperature of Starbucks coffee served on Saturday mornings. (d) The revenue from coffee sales as a percentage of Starbucks' total revenue last year.
a) sample b) census c) sample d) census
Convert each individual data value to a standardized z-score. a-1. Ages of airline passengers: x = 92, μ = 46, σ = 13 (Round your answer to 3 decimal places.) a-2. Is it an outlier? b-1. FICO credit scores: x = 583, μ = 723, σ = 69 (Round your answer to 2 decimal places.) b-2. Is it an outlier? c-1. Condo rental vacancy days: x = 28, μ = 22, σ = 7 (Round your answer to 3 decimal places.) c-2. Is it an outlier?
a. z = (92 − 46)/13 = 3.538. Yes this is an outlier because z > 3. b. z = (583 − 723)/69 = −2.02. Yes, this is an unusual observation because z < −2.0. c. z = (28 − 22)/7 = 0.857. No, this is not an outlier nor is it unusual because −2.0 < z < 2.0.
For each data set, is the mode a good measure of center? a. Genders of 12 CEOs: M, M, F, M, F, M, M, M, F, M, M, M b. Ages of 10 college freshmen: 17, 17, 18, 18, 18, 18, 18, 18, 19, 20 c. Ages of 8 MBA students: 24, 26, 27, 28, 30, 31, 33, 37
a. YES This is attribute data so mode is the only measure of central tendency possible. Mode = M, which occurs 9 out of 12 observations. b. YES This is discrete data with a small range so mode could be an appropriate measure of central tendency. Mode = 18, which occurs 6 out of 10 observations. c. NO There is no mode in this case because there is no value that occurs more than once. Therefore, either mean or median would be more appropriate. Mean = 29.5 and median = 29.
"The probability of rolling three sevens in a row with dice is .0046." Which kind of probability is it? a) empirical b) classical c) subjective
b) classical
Data are collected from 1100 randomly selected students who graduated between 2010 and 2018 from the University of Southern California. Some of the variables that were collected are listed below. Identify which of the following variables is numerical. a) gender of student b) school/college from which student graduated c) annual salary of the first job after graduation d) graduation date in terms of semester (Fall 2010, Spring 2012, etc) e) graduation year (2010, 2012)
c) annual salary of the first job after graduation
The Graduate Management Admission Test (GMAT) is used by many graduate schools of business as one of their admission criteria. Using your own reasoning and concepts in this chapter, criticize each of the following conclusions. Statements a) Last year, 7,573 computer science majors took the GMAT, compared with only 588 philosophy majors. Philosophy majors must not be interested in business because so few take the GMAT." b) "Last year, 29,688 engineering majors took the GMAT, compared with only 3,589 English majors. Clearly, more students major in engineering than in English." c) "Last year, physics majors averaged 100 points higher on the GMAT than marketing majors. If marketing students majored in physics, they would score better on the GMAT." d) "On average, physics majors score higher on the GMAT than accounting majors. Therefore, physics majors would make the best managers." Match the four statements to their appropriate criticism. e) "The GMAT is just one indicator of managerial skill and ability. It is not the only predictor of success in management." f) "This statement suffers from self-selection bias. There are likely many more marketing majors who choose to take the GMAT and therefore may have a wider range of abilities than the abilities of physics majors who choose to take the GMAT." g) "We need to know the total number of philosophy majors to evaluate this." h) "We don't know the number of students in each major from this table." Explanation
d -> e c -> f a -> g b -> h
For which of the following does the random variable X have a binomial distribution? a) X is the number of pastrami sandwiches sold at a deli in a month. b) X is the number of speeding tickets given out at a randomly picked location in a city during a calendar year. c) X is the number of defects found in 100 meters of fiber optic cable. d) X is the number of people in a random sample of size 50 from a large population that have type-AB blood. e) X is the number of tries a kicker makes to score 4 field goals in a football game.
d) X is the number of people in a random sample of size 50 from a large population that have type-AB blood.
For each data set, answer the following questions. Data Set A: 6, 7, 8 Data Set B: 4, 5, 6, 7, 8, 9, 10 Data Set C: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, Find the mean, sample standard deviation-treating the data as a sample, and the population standard deviation-treating the data as a population. (Round your answers to 4 decimal places.) d) What does this exercise show? (Select all that apply) - The sample standard deviation is larger than the population standard deviation for the same data set. - Samples can have similar means but different standard deviations. - The sample standard deviation is smaller than the population standard deviation for the same data set. - Samples can have different means but smaller standard deviations.
data set A: mean: 7.0000 sample st. dev: 1.000 population st. dev: .8165 data set B: mean: 7.0000 sample st. dev: 2.1602 population st. dev: 2.0000 data set C: mean: 7.0000 sample st. dev: 3.8944 population st. dev: 3.7417 d) - The sample standard deviation is larger than the population standard deviation for the same data set. - Samples can have similar means but different standard deviations.
