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AP Statistics Statistics — practice by topic

Browse 217 questions across 13 Statistics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Statistics topics

Sampling and Data (23)The F Distribution and One-Way ANOVA (23)Continuous Random Variables (22)Descriptive Statistics (22)Hypothesis Testing (21)Linear Regression and Correlation (21)The Normal Distribution (21)Probability Topics (20)The Chi-Square Distribution (19)The Central Limit Theorem (18)Discrete Random Variables (5)Confidence Intervals (2)Confidence Intervals for a Mean (2)

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In the notation used for a discrete random variable, what does a lower case letter such as x represent?Read the answer and worked solution →Which three conditions define a geometric experiment?Read the answer and worked solution →A bakery puts an average of 12 loaves of bread on its shelf every 30 minutes. What is the average number of loaves put on the shelf in a five-minute interval?Read the answer and worked solution →An email user receives 147 emails per day on average, so X ~ P(147). What is the standard deviation of the number of emails received in a day?Read the answer and worked solution →

Worked practice questions

In the notation used for a discrete random variable, what does a lower case letter such as x represent?

  1. One specific numerical value the variable takes
  2. The random variable's name, spoken in words
  3. The probability attached to an outcome
  4. The total count of trials performed
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Correct answer: A. One specific numerical value the variable takes

1. Convention reserves upper case X for the random variable itself, written and read in words. 2. Lower case x is used for one particular numerical value that X can take on. 3. Option B describes upper case X, not lower case x, so it is the wrong role. 4. Options C and D describe a probability and a trial count, neither of which is what x denotes. _Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable_

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Which three conditions define a geometric experiment?

  1. Fixed trials, two outcomes, and independent draws
  2. Sampling without replacement from two groups
  3. Events counted over an interval at a known rate
  4. Repeated trials until the first success occurs
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Correct answer: D. Repeated trials until the first success occurs

1. A geometric experiment repeats Bernoulli trials, all failures except the last, which is the success that ends the process. 2. In theory there is no upper limit on how many trials it could take, though there must be at least one. 3. The probability of success, p, and of failure, q, stay the same on every trial. 4. Option A describes a binomial experiment and option C a hypergeometric one, so neither fits the geometric case. _Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_

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A bakery puts an average of 12 loaves of bread on its shelf every 30 minutes. What is the average number of loaves put on the shelf in a five-minute interval?

  1. 12 loaves
  2. 6 loaves
  3. 0.4 loaves
  4. 2 loaves
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Correct answer: D. 2 loaves

1. The rate is 12 loaves per 30 minutes. 2. Scale that rate to a 5-minute window: (5/30)(12) = 2. 3. So the average number of loaves in five minutes is 2, which becomes the μ for a Poisson model of that interval. 4. Option B uses a 15-minute scaling by mistake, and option B forgets to rescale the interval at all. _Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.6 Poisson Distribution_

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