items
Every item in the release, including the broken ones. Filter by arm, construct, requested difficulty, key status or flag group; open any item for the full evidence.
180 of 180 items
| Item | Arm | Subskill | Target | Key | Flags | Stem |
|---|---|---|---|---|---|---|
| REF-BP001-0 | Reference | C01.1 direction of conditioning | medium · CD3 | Pending | — | In a factory audit, it was reported that 55% of the employees who use the shuttle are night-shift workers. Which probability was reported? |
| REF-BP001-1 | Reference | C01.1 direction of conditioning | medium · CD3 | Pending | — | In a factory audit, it was reported that 71% of the employees who use the shuttle are night-shift workers. Which probability was reported? |
| REF-BP001-2 | Reference | C01.1 direction of conditioning | medium · CD3 | Pending | — | In a logistics review, it was reported that 55% of the orders who arrive late are express. Which probability was reported? |
| REF-BP002-0 | Reference | C01.2 conditional from two way table | easy · CD2 | Pending | — | A table from an airline study records 218 passengers. Of the 123 who are frequent flyers, 53 check a bag; of the 95 who are occasional flyers, 52 check a bag. A passenger is chosen |
| REF-BP002-1 | Reference | C01.2 conditional from two way table | easy · CD2 | Pending | — | A table from a clinic record review records 202 patients. Of the 123 who are over 60, 89 report side effects; of the 79 who are under 60, 41 report side effects. A patient is chose |
| REF-BP002-2 | Reference | C01.2 conditional from two way table | easy · CD2 | Pending | — | A table from an airline study records 196 passengers. Of the 117 who are frequent flyers, 83 check a bag; of the 79 who are occasional flyers, 37 check a bag. A passenger is chosen |
| REF-BP003-0 | Reference | C01.3 conditional vs joint | medium · CD3 | Pending | — | A researcher selects one passenger at random from all passengers in an airline study and finds that it is a frequent flyer and that it checks a bag. Which expression gives the prob |
| REF-BP003-1 | Reference | C01.3 conditional vs joint | medium · CD3 | Pending | — | A researcher selects one passenger at random from all passengers in an airline study and finds that it is a frequent flyer and that it checks a bag. Which expression gives the prob |
| REF-BP003-2 | Reference | C01.3 conditional vs joint | medium · CD3 | Pending | — | A researcher selects one patient at random from all patients in a clinic record review and finds that it is over 60 and that it reports side effects. Which expression gives the pro |
| REF-BP004-0 | Reference | C02.1 posterior from screening | hard · CD4 | Pending | — | In a population, 3.0% of people have a rare metabolic disorder. A screening test detects the condition in 95% of people who have it, and correctly returns a negative result for 90% |
| REF-BP004-1 | Reference | C02.1 posterior from screening | hard · CD4 | Pending | — | In a population, 0.5% of people have an early-stage infection. A screening test detects the condition in 99% of people who have it, and correctly returns a negative result for 96% |
| REF-BP004-2 | Reference | C02.1 posterior from screening | hard · CD4 | Pending | — | In a population, 1.0% of people have an early-stage infection. A screening test detects the condition in 92% of people who have it, and correctly returns a negative result for 94% |
| REF-BP005-0 | Reference | C02.2 base rate reasoning | hard · CD3 | Pending | 1 cue | A condition affects 0.5% of a population. A test is 99% accurate in both directions. Among everyone who tests positive, fewer than one in ten actually has the condition. Which stat |
| REF-BP005-1 | Reference | C02.2 base rate reasoning | hard · CD3 | Pending | 1 cue | A condition affects 0.2% of a population. A test is 98% accurate in both directions. Among everyone who tests positive, fewer than one in ten actually has the condition. Which stat |
| REF-BP005-2 | Reference | C02.2 base rate reasoning | hard · CD3 | Pending | 1 cue | A condition affects 0.2% of a population. A test is 99% accurate in both directions. Among everyone who tests positive, fewer than one in ten actually has the condition. Which stat |
| REF-BP006-0 | Reference | C03.1 test independence from table | medium · CD4 | Pending | — | In an airline study, 500 passengers were classified. Among the 200 frequent flyers, 60 check a bag; among the 300 occasional flyers, 90 check a bag. Is being a frequent flyer indep |
| REF-BP006-1 | Reference | C03.1 test independence from table | medium · CD4 | Pending | — | In a municipal survey, 400 households were classified. Among the 240 rural, 96 subscribe to broadband; among the 160 urban, 64 subscribe to broadband. Is being rural independent of |
| REF-BP006-2 | Reference | C03.1 test independence from table | medium · CD4 | Pending | — | In an airline study, 500 passengers were classified. Among the 200 frequent flyers, 136 check a bag; among the 300 occasional flyers, 96 check a bag. Is being a frequent flyer inde |
| REF-BP007-0 | Reference | C03.2 independent vs mutually exclusive | easy · CD3 | Pending | — | Events A and B each have positive probability: P(A) = 0.3 and P(B) = 0.6. A and B are mutually exclusive. Which statement follows? |
| REF-BP007-1 | Reference | C03.2 independent vs mutually exclusive | easy · CD3 | Pending | — | Events A and B each have positive probability: P(A) = 0.4 and P(B) = 0.5. A and B are mutually exclusive. Which statement follows? |
| REF-BP007-2 | Reference | C03.2 independent vs mutually exclusive | easy · CD3 | Pending | — | Events A and B each have positive probability: P(A) = 0.4 and P(B) = 0.5. A and B are mutually exclusive. Which statement follows? |
| REF-BP008-0 | Reference | C04.1 addition rule with overlap | easy · CD2 | Pending | — | In a municipal survey, the probability that a randomly chosen household is rural is 0.33, the probability that it subscribes to broadband is 0.45, and the probability that both are |
| REF-BP008-1 | Reference | C04.1 addition rule with overlap | easy · CD2 | Pending | — | In a university survey, the probability that a randomly chosen student is a commuter is 0.4, the probability that it owns a bicycle is 0.52, and the probability that both are true |
| REF-BP008-2 | Reference | C04.1 addition rule with overlap | easy · CD2 | Pending | — | In a factory audit, the probability that a randomly chosen employee is a night-shift worker is 0.36, the probability that it uses the shuttle is 0.48, and the probability that both |
| REF-BP009-0 | Reference | C04.2 complement rule | medium · CD2 | Pending | — | In a clinic record review, each patient independently reports side effects with probability 0.08. 6 patients are selected at random. What is the probability that at least one of th |
| REF-BP009-1 | Reference | C04.2 complement rule | medium · CD2 | Pending | — | In an airline study, each passenger independently checks a bag with probability 0.08. 6 passengers are selected at random. What is the probability that at least one of them checks |
| REF-BP009-2 | Reference | C04.2 complement rule | medium · CD2 | Pending | — | In an airline study, each passenger independently checks a bag with probability 0.25. 3 passengers are selected at random. What is the probability that at least one of them checks |
| REF-BP010-0 | Reference | C05.1 expectation from pmf | easy · CD2 | Pending | — | A discrete random variable X has the distribution P(X = 1) = 0.12; P(X = 5) = 0.5; P(X = 7) = 0.25; P(X = 8) = 0.13. What is the expected value E[X]? |
| REF-BP010-1 | Reference | C05.1 expectation from pmf | easy · CD2 | Pending | — | A discrete random variable X has the distribution P(X = 0) = 0.12; P(X = 1) = 0.5; P(X = 4) = 0.12; P(X = 7) = 0.26. What is the expected value E[X]? |
| REF-BP010-2 | Reference | C05.1 expectation from pmf | easy · CD2 | Pending | — | A discrete random variable X has the distribution P(X = 2) = 0.1; P(X = 4) = 0.4; P(X = 5) = 0.3; P(X = 6) = 0.2. What is the expected value E[X]? |
| REF-BP011-0 | Reference | C05.2 linearity of expectation | easy · CD2 | Pending | — | The number of hours X for a repair job has mean E[X] = 8. The invoice in dollars is Y = 5X + 10. What is E[Y]? |
| REF-BP011-1 | Reference | C05.2 linearity of expectation | easy · CD2 | Pending | — | The number of hours X for a repair job has mean E[X] = 15. The invoice in dollars is Y = 4X + 40. What is E[Y]? |
| REF-BP011-2 | Reference | C05.2 linearity of expectation | easy · CD2 | Pending | — | The number of hours X for a repair job has mean E[X] = 20. The invoice in dollars is Y = 2.5X + 20. What is E[Y]? |
| REF-BP012-0 | Reference | C06.1 variance from pmf | medium · CD2 | Pending | — | A discrete random variable X has the distribution P(X = 1) = 0.29; P(X = 4) = 0.14; P(X = 5) = 0.29; P(X = 6) = 0.28. What is Var(X)? |
| REF-BP012-1 | Reference | C06.1 variance from pmf | medium · CD2 | Pending | — | A discrete random variable X has the distribution P(X = 0) = 0.27; P(X = 1) = 0.18; P(X = 7) = 0.36; P(X = 8) = 0.19. What is Var(X)? |
| REF-BP012-2 | Reference | C06.1 variance from pmf | medium · CD2 | Pending | — | A discrete random variable X has the distribution P(X = 0) = 0.31; P(X = 1) = 0.31; P(X = 5) = 0.08; P(X = 6) = 0.3. What is Var(X)? |
| REF-BP013-0 | Reference | C06.2 variance under linear transform | medium · CD2 | Pending | — | A random variable X has standard deviation 1.5. Define Y = 4X + 10. What is Var(Y)? |
| REF-BP013-1 | Reference | C06.2 variance under linear transform | medium · CD2 | Pending | — | A random variable X has standard deviation 1.5. Define Y = 4X + 40. What is Var(Y)? |
| REF-BP013-2 | Reference | C06.2 variance under linear transform | medium · CD2 | Pending | — | A random variable X has standard deviation 2. Define Y = 2.5X + 25. What is Var(Y)? |
| REF-BP014-0 | Reference | C07.1 binomial point probability | medium · CD2 | Pending | — | In a factory audit, each employee independently uses the shuttle with probability 0.3. For a random sample of 12 employees, what is the probability that exactly 3 of them use the s |
| REF-BP014-1 | Reference | C07.1 binomial point probability | medium · CD2 | Pending | — | In a municipal survey, each household independently subscribes to broadband with probability 0.25. For a random sample of 12 households, what is the probability that exactly 4 of t |
| REF-BP014-2 | Reference | C07.1 binomial point probability | medium · CD2 | Pending | — | In an airline study, each passenger independently checks a bag with probability 0.4. For a random sample of 10 passengers, what is the probability that exactly 2 of them check a ba |
| REF-BP015-0 | Reference | C07.2 binomial cumulative | hard · CD4 | Pending | — | In a municipal survey, each household independently subscribes to broadband with probability 0.3. In a random sample of 8 households, what is the probability that at most 2 of them |
| REF-BP015-1 | Reference | C07.2 binomial cumulative | hard · CD4 | Pending | — | In an airline study, each passenger independently checks a bag with probability 0.35. In a random sample of 12 passengers, what is the probability that at most 3 of them check a ba |
| REF-BP015-2 | Reference | C07.2 binomial cumulative | hard · CD4 | Pending | — | In an airline study, each passenger independently checks a bag with probability 0.4. In a random sample of 12 passengers, what is the probability that at most 4 of them check a bag |
| REF-BP016-0 | Reference | C07.3 binomial conditions | hard · CD3 | Pending | — | Which random variable X has a binomial distribution? |
| REF-BP016-1 | Reference | C07.3 binomial conditions | hard · CD3 | Pending | — | Which random variable X has a binomial distribution? |
| REF-BP016-2 | Reference | C07.3 binomial conditions | hard · CD3 | Pending | — | Which random variable X has a binomial distribution? |
| REF-BP017-0 | Reference | C08.1 zscore computation | easy · CD2 | Pending | — | The germination time of a population is normally distributed with mean 9 days and standard deviation 1.5 days. What is the z-score of a value of 12 days? |
| REF-BP017-1 | Reference | C08.1 zscore computation | easy · CD2 | Pending | — | The commute time of a population is normally distributed with mean 34 minutes and standard deviation 8 minutes. What is the z-score of a value of 50 minutes? |