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AP Statistics The Normal Distribution — practice questions

Explore 21 free The Normal Distribution questions in AP Statistics Statistics. Open each question or exercise to read its content, reference answers and available explanation.

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The Normal Distribution questions and exercises with answers

Showing questions 1–21 of 21.

The standard normal distribution is a normal distribution of standardized values called:Read the answer and worked solution →The empirical rule is also known as the:Read the answer and worked solution →About what percentage of values lie within two standard deviations of the mean?Read the answer and worked solution →About what percentage of values lie within three standard deviations of the mean?Read the answer and worked solution →The total area under a normal probability curve must equal:Read the answer and worked solution →Increasing the standard deviation of a normal distribution makes the curve:Read the answer and worked solution →A z-score of plus 1 marks the value that is:Read the answer and worked solution →Converting to the standard normal distribution lets you:Read the answer and worked solution →Between one standard deviation and two, the extra share of values captured is about:Read the answer and worked solution →The z-scores that bound the middle 99.7 percent of a normal distribution are:Read the answer and worked solution →A normal distribution is often described by the shape of its curve as:Read the answer and worked solution →Two normal curves with different standard deviations must still have equal:Read the answer and worked solution →A z-score of zero corresponds to a value that is:Read the answer and worked solution →If about 68 percent of values lie within one standard deviation, the share lying outside three deviations is roughly:Read the answer and worked solution →The z-scores minus 2 and plus 2 correspond to which pair of original values in a distribution with mean 50 and deviation 6?Read the answer and worked solution →Recognising the standard normal distribution matters because it can then be:Read the answer and worked solution →Match each z-score to its shareRead the answer and worked solution →Key in the empirical ruleRead the answer and worked solution →True or false: the normal curveRead the answer and worked solution →Which band holds more data?Read the answer and worked solution →Complete the standardising ruleRead the answer and worked solution →

Worked practice questions

The standard normal distribution is a normal distribution of standardized values called:

  1. Z-scores
  2. T-scores
  3. P-values
  4. Raw scores
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Correct answer: A. Z-scores

1. Standardising puts every normal distribution on one common scale. 2. The standard normal distribution is a normal distribution of standardized values. 3. Those standardized values are called z-scores. 4. A t-score belongs to a different distribution used when the population deviation is unknown. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 6 'The Normal Distribution', sections 6.1-6.3_

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The empirical rule is also known as the:

  1. 10-20-30 rule
  2. 68-95-99.7 rule
  3. 50-75-90 rule
  4. 25-50-75 rule
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Correct answer: B. 68-95-99.7 rule

1. The rule states how much of a normal distribution falls within one, two and three deviations. 2. The empirical rule is also known as the 68-95-99.7 rule. 3. Each number in that name is a cumulative percentage. 4. The numbers correspond to one, two and three standard deviations respectively. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 6 'The Normal Distribution', sections 6.1-6.3_

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About what percentage of values lie within two standard deviations of the mean?

  1. 99.7 percent
  2. 50 percent
  3. 95 percent
  4. 68 percent
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Correct answer: C. 95 percent

1. The empirical rule assigns a percentage to each distance from the mean. 2. About 95 percent of the x values lie within two standard deviations of the mean. 3. The z-scores at those two points are minus 1 and plus 1 for one deviation, and minus 2 and plus 2 for two. 4. 68 percent is the figure for one standard deviation instead. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 6 'The Normal Distribution', sections 6.1-6.3_

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