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AP Statistics Continuous Random Variables — practice questions

Explore 22 free Continuous Random Variables questions in AP Statistics Statistics. Open each question or exercise to read its content, reference answers and available explanation.

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Continuous Random Variables questions and exercises with answers

Showing questions 1–22 of 22.

For a continuous random variable, probability is represented by:Read the answer and worked solution →The curve used to draw a continuous probability distribution is called the:Read the answer and worked solution →Which symbol is used to represent the density curve?Read the answer and worked solution →Area under the curve is given by which function?Read the answer and worked solution →For a continuous random variable, the probability that x takes on any single value is:Read the answer and worked solution →The heights of radish plants are given as an example of which kind of variable?Read the answer and worked solution →Which three distributions are named for study in these chapters?Read the answer and worked solution →The notation for the uniform distribution is written as:Read the answer and worked solution →In the notation X ~ U(a, b), the letter a stands for:Read the answer and worked solution →In the notation X ~ U(a, b), the letter b stands for:Read the answer and worked solution →The probability P(c < x < d) is the area under the curve, above the x-axis, and:Read the answer and worked solution →Calculations with the exponential distribution require knowledge of which quantity?Read the answer and worked solution →The exponential distribution's memorylessness means past waiting time affects future waiting:Read the answer and worked solution →Because P(x = c) is zero for a continuous variable, P(c < x < d) and P(c <= x <= d) are:Read the answer and worked solution →If X ~ U(0, 10), the probability that x lies between 2 and 4 comes from the area that is:Read the answer and worked solution →The pdf and the cdf differ in that the cdf gives:Read the answer and worked solution →Finding the 90th percentile of a smiling-time distribution means finding the value below which lies:Read the answer and worked solution →Match each continuous termRead the answer and worked solution →True or false: continuous variablesRead the answer and worked solution →Tap what belongs to each ideaRead the answer and worked solution →Complete the continuous rulesRead the answer and worked solution →Stop on the right functionRead the answer and worked solution →

Worked practice questions

For a continuous random variable, probability is represented by:

  1. Area under the curve
  2. Height of the curve
  3. Slope of the curve
  4. Length of the axis
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Correct answer: A. Area under the curve

1. Continuous variables need a different picture from discrete ones. 2. The distribution of a continuous variable is drawn as a curve. 3. Probability is represented by area under the curve. 4. So a wider interval covers more area and more probability. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 5 'Continuous Random Variables', sections 5.1-5.3_

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The curve used to draw a continuous probability distribution is called the:

  1. Residual scatter diagram
  2. Probability density function
  3. Cumulative frequency table
  4. Sample correlation matrix
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Correct answer: B. Probability density function

1. The curve itself has a formal name. 2. The symbol f of x represents the curve. 3. The curve is called the probability density function, abbreviated pdf. 4. The density function is used to draw the graph of the probability distribution. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 5 'Continuous Random Variables', sections 5.1-5.3_

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Which symbol is used to represent the density curve?

  1. f(x)
  2. P(A)
  3. S(n)
  4. R(t)
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Correct answer: A. f(x)

1. The density function has a standard notation. 2. The symbol f of x is used to represent the curve. 3. It is the function that corresponds to the graph. 4. The density function f of x is used to draw the graph of the distribution. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 5 'Continuous Random Variables', sections 5.1-5.3_

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More Statistics topics

Sampling and DataThe F Distribution and One-Way ANOVADescriptive StatisticsHypothesis TestingLinear Regression and CorrelationThe Normal DistributionProbability TopicsThe Chi-Square Distribution