A quality manager divides a day's output into 12 boxes, randomly picks 3 boxes, and inspects every item in those boxes. What sampling method is this?

A principal separates students by grade level, randomly selects 25 students from each grade, and surveys those students about lunch choices. What sampling method is this?

A stadium usher chooses a random starting seat in a row and then surveys every 10th seat after that. What sampling method is this?

A club president surveys the first 30 students who enter the cafeteria before school about a dance theme. What sampling method is this?

A town survey asks, "Do you agree that the wasteful new parking fee should be repealed?" What kind of bias is built into this question?

A school posts an online survey about homework, but many families in the district do not have reliable internet access. What bias is most likely?

A researcher mails 1,000 surveys to voters, but only 80 people return them. What kind of bias is the main concern?

A radio host asks listeners to text whether the city should build a new pool, then reports the results as public opinion. What bias is most likely?

A teacher flips a coin for each of 60 students to decide whether they use a review app or paper notes, then compares exam scores. What kind of study is this?

A clinic records whether 200 patients already exercise regularly and compares their blood pressure without assigning anyone to exercise. What kind of study is this?

A farmer randomly assigns 12 garden plots to three fertilizer formulas and measures crop mass after one month. What kind of study is this?

A tutoring trial puts the first 40 arrivals in online tutoring and the next 40 arrivals in in-person tutoring. Which design principle is missing?

A study has every student use a new flash-card app, then compares their later scores with no other group. Which part of the design is missing?

A sleep study randomly assigns 2 students to caffeine and 2 students to no caffeine, then compares quiz scores. Which design principle is weakest?

A fertilizer trial assigns plants to formulas but never records growth, color, or mass after treatment. Which design part is missing?

In a headache medicine trial, one group gets the real pill and another gets an identical inactive pill. What is the inactive pill called?

In a pain study, neither the patients nor the nurses rating pain know who received the real medicine. What design feature is this?

A study finds that students who drink more energy drinks sleep less, but those students also have later work shifts. What are work shifts in this study?

Before assigning two math programs, a district groups students by previous algebra score and then randomizes within each group. What design strategy is used?

Each cyclist tries tire A and tire B on the same course, with tire order randomized for each cyclist. Times are compared within each cyclist. What design is this?

A blood pressure drug trial blocks by clinic before randomizing patients to drug or placebo. Why use clinic as a block?

A researcher surveys a random sample of all seniors in one district about sleep hours, with no treatment assigned. What inference is supported?

A migraine study uses 100 volunteers and randomly assigns them to a new medicine or a placebo. What inference is supported?

An analyst surveys her friends and finds an association between phone use and grades, with no treatment assigned. What inference is supported?

A fair six-sided die is rolled once. What is the probability of rolling 2, 4, or 6, as a decimal to three places?

A fair coin is flipped twice and the sequence is recorded. What is the probability of getting at least one head, as a decimal to three places?

A bag has 5 red marbles, 3 blue marbles, and 2 green marbles. One marble is drawn at random. What is the probability it is blue, to three decimals?

A spinner has 8 equal sectors, with 3 yellow sectors. What is the probability of landing on yellow, as a decimal to three places?

A machine runs a full day without a fault with probability 0.920. What is the probability it has at least one fault that day?

The probability of rain tomorrow is 0.350. What is the probability it does not rain tomorrow?

A shipment has no defective parts with probability 0.780. What is the probability the shipment has at least one defective part?

For students at a school, the probability of taking art is 0.400, taking music is 0.300, and taking both is 0.120. What is the probability of art or music?

One card is drawn from a standard 52-card deck. What is the probability the card is a queen or a spade, to three decimals?

Use the Venn diagram for 80 students, where B means band and S means sports. What is the probability a student is in band or sports, to three decimals?

Two independent safety switches work with probabilities 0.700 and 0.800. What is the probability both switches work, to three decimals?

At a tryout, 60% of athletes make the first cut. Of those athletes, 50% make the final roster. What is the probability an athlete makes both cuts?

A sensor has no alert on a day with probability 0.850. Alerts on different days are independent. What is the probability of no alert on both Monday and Tuesday?

In a school, 45% of students take art, 30% take choir, and 18% take both. Given that a student takes art, what is the probability the student takes choir?

Among 120 students, 50 ride the bus, 84 arrive on time, and 35 both ride the bus and arrive on time. Given bus rider, what is the probability of arriving on time?

In a clinic, 4% of patients have an allergy, 10% test positive, and 3.5% both have the allergy and test positive. Given a positive test, what is the probability of allergy?

Use the two-way table of travel choices. Given that a student is in grade 11, what is the probability the student rides the bus, to three decimals?

Use the probability tree for shopping path. What is the probability that a shopper buys online and uses a coupon, to three decimals?

Use the screening-test tree. What is the probability that a randomly chosen person tests positive, to three decimals?

A uniform has 4 shirt choices, 3 pants choices, and 2 shoe choices. How many different uniforms are possible?

A cafeteria meal has 5 main dishes, 4 sides, and 3 drinks. If one of each is chosen, how many meals are possible?

A shelf has 6 different books. In how many orders can all 6 books be arranged on the shelf?

A class has 10 volunteers for a 3-person committee, and all committee roles are the same. How many committees are possible?

A basketball player makes 70% of free throws. A simulation uses random digits 0 to 9 for one shot. How many digits should represent a make?

A student simulates rolling a fair die by generating random integers 1 to 6. What is the main effect of increasing from 500 trials to 5,000 trials?

A warranty repair costs $0 with probability 0.700, $50 with probability 0.200, and $200 with probability 0.100. What is the expected repair cost?

A quiz bonus gives 0 points with probability 0.200, 1 point with probability 0.500, and 2 points with probability 0.300. What is the expected bonus?

A carnival game costs $4 to play. It pays $10 with probability 0.100, $2 with probability 0.300, and $0 otherwise. What is the expected net gain per play?

A random variable X can be 0, 1, 2, or 3. Its probabilities for 0, 1, and 2 are 0.25, 0.40, and 0.20. What probability must go with 3?

A factory samples 15 bottles from a very large line where 8% are underfilled, and X counts underfilled bottles. Which fact makes a binomial model reasonable?

A free throw shooter makes each shot independently with probability 0.400. In 5 shots, what is the probability of exactly 2 makes, to three decimals?

A bus is late on 10% of school days, independently. In 6 days, what is the probability it is late exactly once, to three decimals?

In a large batch, 30% of seeds fail to germinate. For 40 randomly chosen seeds, what is the mean number that fail to germinate?

A multiple-choice quiz has 25 questions, and a student guesses each answer with success probability 0.200. What is the standard deviation of the number correct?

A customer buys a raffle ticket each week with winning probability 0.200, independently. What is the probability the first win occurs on week 4, to three decimals?

A player makes each target shot independently with probability 0.250. What is the expected number of attempts up to and including the first make?