Practice Test 8 - Statistics and Probability

20 questions. Answer them in any order, then submit to see your score and every explanation.

Start practice test

1. In a PE class, students reported whether they prefer team sports or individual sports and whether they participate in a school sport team. The results are shown in the two-way table. Which statement best describes the association between participation on a school sport team and sports preference?

   	Prefer Team Sports	Prefer Individual Sports	Total
   On School Team: Yes	48	12	60
   On School Team: No	30	60	90
   Total	78	72	150

2. A game costs $3 to play. It pays $8 with probability 0.4, otherwise $0. What is the expected net gain?
3. A company reports that the time (in minutes) to complete a certain routine task is approximately normal for trained workers. Times are modeled as $N(\mu=30,\,\sigma=4)$. Approximately what percent of workers take between 22 and 38 minutes? (Use the empirical rule.)
4. A student newspaper claims: "Students are spending less time on homework this year." It reports that, in an online poll linked on the newspaper's social media, 65% of 200 respondents said they spend "under 1 hour" on homework per night. Last year, a similar poll had 55% of 220 respondents choose "under 1 hour." Which critique best evaluates the claim?
5. School context: Two events are defined. Event A: a student is late to first period at least once this month. Event B: a student rides the school bus. The assistant principal says, "Bus riders are late more often than non-bus riders." Which statement best describes whether A and B are independent?
6. According to $S=\{1,2,3,4,5,6,7,8\}$, a number is chosen at random. Event $A$ is the event that the number is even. Event $B=\{x\in S\mid x>5\}$. Which expression represents $A\cap B$ (A and B)?
7. A product features audit defines event $A$ as "a laptop has a touchscreen" and event $B$ as "a laptop has a backlit keyboard." The audit reports $P(A)=0.36$, $P(B)=0.50$, and $P(A\cap B)=0.22$. What is the probability that a laptop has a touchscreen or a backlit keyboard (inclusive or)?
8. A player can choose one of two strategies each time they play a carnival game. Strategy A: Pay $4 to play. Outcomes: with probability 0.70 you win $6; with probability 0.30 you win $0. Strategy B: Pay $4 to play. Outcomes: with probability 0.20 you win $20; with probability 0.80 you win $0. Over many repetitions, which strategy has the greater expected value (net profit in dollars)?
9. A health app compares daily step count (steps) and daily calories burned (calories) for one user over many days. A scatter plot shows a roughly linear upward trend, and technology reports $r=0.88$. Which statement best interprets the value of $r$ for the relationship between steps and calories burned?
10. A store recorded 18 customer wait times (in minutes): 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 12, 14. Which plot best represents the data as a histogram using bin width 5 minutes with bins 0–4, 5–9, 10–14?
11. A gym chain wants to estimate the mean number of visits per month among all members at one specific location. From the list of all members at that location, the manager randomly selects 40 members and records their number of visits last month. Which statement best distinguishes the parameter from the statistic in this situation?
12. A company tested a new keyboard by randomly assigning office workers to use either the new keyboard or their usual keyboard for 2 weeks. The workers assigned to the new keyboard typed more words per minute on average at the end of the study. Which statement is the most reasonable conclusion?
13. A random sample of 90 students was surveyed about whether they prefer working on projects or tests and whether they report studying at least 5 hours per week. Using the two-way table, estimate the probability that a randomly selected student studies at least 5 hours per week given that the student prefers projects. Give your answer as a percent. Two-way table (counts): - Rows: Assessment preference (Projects, Tests) - Columns: Studies $\ge 5$ hours/week (Yes, No) Projects: Yes 24, No 21 (Row total 45) Tests: Yes 18, No 27 (Row total 45) Column totals: Yes 42, No 48, Grand total 90
14. Each play costs $2. A play pays $10 with probability .25, else $0. What is the expected net profit for 5 plays?
15. A museum randomly assigned 66 visitors to two audio guide options: Treatment A (short highlights) and Treatment B (full-length tour), with 33 visitors in each group. After the visit, each person took a 12-question quiz about the exhibits. Treatment A had a mean score of 9.8 and Treatment B had a mean score of 10.1, so the observed difference in means was $9.8-10.1=-0.3$ (A − B). To test whether Treatment A produces lower scores than Treatment B, the museum ran a randomization test by shuffling labels 4000 times and computing (A − B). In the simulations, 12 of the 4000 shuffled differences were $\le -0.3$ (at least as extreme in the direction of A being lower). Which conclusion is most reasonable about the treatment effect?
16. Two marbles are drawn from a bag with replacement. Let event $A$ be "the first marble is red" and event $B$ be "the second marble is red." Given that $P(A)=0.2$, $P(B)=\tfrac{1}{5}$, and $P(A\cap B)=0.04$, are $A$ and $B$ independent? Justify using probabilities.
17. A survey asks respondents about two preferences. Event $A$ is "a respondent prefers tea," and event $B$ is "a respondent prefers coffee." The results show $P(A)=0.48$, $P(B)=0.52$, and $P(A\cap B)=0.20$ (respondents who prefer both). What is the probability that a respondent prefers tea or coffee (inclusive)?
18. A library wants to estimate the average number of books checked out per student each month. They randomly select 200 student ID numbers from the school database and then use library records to find how many books each selected student checked out last month. No students are contacted. Which type of study is described?
19. A company compared the number of years an employee has worked at the company (x) and the employee's annual salary in dollars (y). Technology reports $r=0.95$. Which statement best interprets the value of $r$?
20. A 4-digit code is formed by arranging 4 different digits chosen from $\{0,1,2,3,4,5,6\}$. Digits cannot repeat, and order matters because different arrangements make different codes. All such codes are equally likely. What is the probability that the code starts with 0?

Practice tests