AP Statistics Discrete Random Variables — practice questions
58 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP Statistics Discrete Random Variables in the app →In the notation used for a discrete random variable, what does a lower case letter such as x represent?A statistics class tosses a coin three times and lets X count the heads. Why is X called a discrete random varWhat two conditions must a table of x and P(x) values satisfy to count as a discrete probability distribution A hospital researcher records X = the number of times a post-op patient rings the nurse in a 12-hour shift, foA physics-major table lists P(x=1)=0.35, P(x=2)=0.20, P(x=3)=0.15, P(x=5)=0.10, P(x=6)=0.05, with P(x=4) left A table gives P(x=1)=0.15, P(x=2)=0.25, P(x=3)=0.30, P(x=4)=0.20, P(x=5)=0.15. What is wrong with this probabiNancy attends her three weekly classes on all three days 80% of the time, two days 15% of the time, one day 4%Using the standard rule for computing an expected value, how do you find the mean, μ, of a discrete random varA men's soccer team plays zero days a week with probability 0.2, one day with probability 0.5, and two days wiFor the newborn-crying example, a child psychologist finds μ = 2.1 times per week that crying wakes the motherIn a $2-to-play game, a computer draws five digits with replacement, and matching all five in order pays $100,In a coin game, P(heads) = 2/3 and P(tails) = 1/3. Tossing heads costs you $6 and tossing tails wins you $10. A fair six-sided die is tossed twice, and X counts the number of the two faces that show an even number. UsingOn May 11, 2013, the chance of one moderate earthquake in Iran over the next 48 hours was reported at about 21Karl Pearson once tossed a fair coin 24,000 times and recorded 12,012 heads, a demonstration of a key statistiYou draw a card from a 52-card deck and replace it. A face card (12 of the 52 cards) wins $30; any other card In a card-and-coin game, a face card with heads wins $6 (probability 6/52), a face card with tails wins $2 (prThe mean of a probability distribution is defined using the symbol μ and the formula μ = Σ x P(x). What role dWhich set of three conditions must a statistical experiment satisfy to be classified as binomial?Why does the outcome of one trial in a binomial experiment fail to help predict the outcome of another trial?A binomial experiment with exactly n = 1 trial, satisfying the two-outcome and constant-probability conditionsAt ABC College the withdrawal rate from an elementary physics course is 30% every term, so 70% of students finAn ABC College committee of ten staff and six students draws two names without replacement, one becomes chairpAbout 41% of adult workers have a high school diploma but pursue no further education. For a random sample of In a 560-page art catalog, 8 pages feature signature artists. Sampling 100 pages gives X ~ B(100, 8/560). UsinThe lifetime risk of pancreatic cancer is about 1.28%. For a random sample of 200 people, X ~ B(200, 0.0128) cFor pancreatic cancer risk X ~ B(200, 0.0128), a binomial calculator gives P(x=5) = 0.0707 and P(x=6) = 0.0298The San Jose Sharks win any given game with probability 0.3694, based on 382 wins out of 1,034 games. Over an For the San Jose Sharks example, X ~ B(12, 0.3694) counts wins in 12 games. Using the binomial formula, what iIn Afghanistan the literacy rate is 28.1%. For a random sample of 15 people, X ~ B(15, 0.281). What are the meFor the Afghanistan literacy example, X ~ B(15, 0.281) gives P(x=3) = 0.1927 and P(x=4) = 0.2259. Is it more lA student randomly guesses on a 32-question multiple-choice exam where each question has three choices, so X ~A student takes a ten-question true-false quiz and guesses randomly at every answer, so X ~ B(10, 0.5). What iAt the Fencing Center, 60% of fencers use the foil. Surveying 25 fencers at random, X ~ B(25, 0.40) counts thoA rule of thumb governs when the Poisson distribution can approximate a binomial distribution. According to thWhich three conditions define a geometric experiment?Someone throws darts at a bullseye repeatedly until the first hit, which is described as failure, failure, faiFor a geometric random variable X ~ G(p), formulas exist for its mean and standard deviation. What are they?The probability of a defective computer component is 0.02, so X ~ G(0.02) counts components tested until the fWith defective-component probability p = 0.02, using the geometric formula P(X=x) = p(1-p)^(x-1), what is P(x=The lifetime risk of pancreatic cancer is about 1.28%. Let X ~ G(0.0128) count how many people you must ask un40% of adults will watch the Super Bowl, so X ~ G(0.40) counts how many adults must be surveyed until one who 75% of millennials have a profile on a social networking site. Let X ~ G(0.25) count how many millennials you A college student contacts classmates at random, one at a time, until one confirms living within five miles, wFor the millennial social-media example, X ~ G(0.25) counts people asked until finding one without a profile, Which two characteristics define a Poisson experiment?A Poisson random variable is written X ~ P(μ). What are the mean, variance, and standard deviation of X in terA bakery puts an average of 12 loaves of bread on its shelf every 30 minutes. What is the average number of loLeah's answering machine receives about six calls between 8 a.m. and 10 a.m., a two-hour window. Rescaled to μAn email user receives 147 emails per day on average, so X ~ P(147). What is the standard deviation of the numText message users send or receive an average of 41.5 texts per day. Converted to an hourly rate of about 1.72For 200 days with a 1.02% chance of low seismic activity per day in Alaska, the binomial model gives P(x=10) ≈A manufacturer finds 3% of its Christmas light bulbs defective. For a string of 100 lights, the Poisson model The chance of an IRS audit for a return over $25,000 is about 2% per year. For 100 such taxpayers in one year,Continuing the IRS audit example with X ~ P(2), what is P(x≥3), the probability that at least three of the 100Pierre, an amateur chef, drops an average of 1.5 pieces of egg shell into each cake he bakes, so X ~ P(1.5). IThe average number of children a Spanish woman has in her lifetime is 1.47, so X ~ P(1.47). What is P(x=0), thMrs. Plum's cats wake her up an average of ten times per week, so X ~ P(10). What is P(x≤5), the probability h