Questions and Answers
What is the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed?
0.28
What is the probability that 8 of the selected young adults will expect to bring work on a vacation trip?
(20/8)(0.74)^8(0.26)^12
What is the probability that fewer than 8 of the selected adults wear glasses or contact lenses?
0.47
What is the closest to the standard deviation of W, the number of workers who arrive to work between 6:45 A.M. and 7:00 A.M.?
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By how much will the mean of M exceed the mean of B?
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What is the expected value of the number in the sample enrolled in college?
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What is the best interpretation of the random variable T representing the number of electrical transformers operating during a severe storm?
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What is the best interpretation of random variable R, representing the number of people who answer yes to having read a novel?
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What does the value of (40/8)(0.1)^8(0.9)^32 describe?
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What is the closest to the probability that it will take 5 selections to find one delayed flight?
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What is the probability that the representative must select 4 attendees to find one who is left-handed?
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What is the expected number of residents the researcher will need to ask to find someone who has seen the production?
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What is the closest to the standard deviation of random variable K, which has a geometric distribution with mean 16?
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What is the best interpretation of the mean of random variable Y representing homes selected until a home with solar panels is found?
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What is the best interpretation of the expected value of the number of orders placed until the first daily special is ordered?
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Study Notes
Thumbtack Simulation
- Probability of a thumbtack landing point up is 0.2.
- Simulation results suggest the probability of at least 2 tacks landing point up is approximately 0.28.
Young Adult Work Expectations
- In 2018, 74% of employed young adults expected to work while on vacation.
- Probability formula for exactly 8 out of 20 young adults: (20 choose 8) × (0.74)^8 × (0.26)^12.
Glasses or Contact Lenses Usage
- In the U.S., 75% of adults wear glasses or contacts.
- Probability that fewer than 8 out of 10 adults wear glasses/contact lenses is about 0.47.
Workers' Arrival Times
- In 2016, 6% of workers arrived at work between 6:45 A.M. and 7:00 A.M.
- For 300 workers sampled, the standard deviation of arrivals during this timeframe is approximately 4.11.
Population Demographics
- 18% of the U.S. population are baby boomers; 27% are millennials.
- In a sample of 500, the mean difference between millennials and baby boomers is about 45.
College Enrollment in Baltimore County
- In 2015, 75,511 out of 822,959 residents were enrolled in college.
- In a sample of 800 residents, expected number of college enrollees is approximately 73.4.
Electrical Transformers Performance
- 85% operational time for electrical transformers during storms.
- A sample of 20 transformers yields a mean of 17 operational transformers and a standard deviation of about 2.55.
Novel Reading Frequency
- Random sample of people asked about novel reading yields variance of 6.
- Represents a binomial variable with 25 independent trials based on a 0.40 reading proportion.
Returns at a Department Store
- 10% of customers are expected to return merchandise.
- Probability formula for 8 returns in a sample of 40 customers: (40 choose 8) × (0.1)^8 × (0.9)^32.
Flight Delays
- 15% of flights for a certain airline are delayed.
- Probability that it takes 5 selections to find a delayed flight is approximately 0.0783.
Probability of Finding Left-Handed Person
- 10% of convention attendees are left-handed.
- Probability must select 4 attendees to find one left-handed person: 0.1 × (0.9^3).
Theater Production Awareness
- Approximately 9% of residents have seen a specific theater production.
- Expected number of residents to ask to find someone who has seen the production is about 11.11.
Geometric Distribution Characteristics
- Random variable K has a mean of 16; its standard deviation is closest to 15.49.
- Random variable Y, representing homes with solar panels, has a mean of 10, indicating it takes on average 10 selections to find one.
Daily Special Orders at Restaurant
- 35% of customers at a restaurant order the daily special.
- Expected value of 2.86 orders needed before the first special order reflects average customer behavior over time.
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Description
Test your knowledge on the probability concepts covered in AP Statistics Unit 4. This quiz focuses on simulations, statistical trials, and interpretation of results. Ideal for students preparing for exams or progressing through the AP Stat curriculum.
