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AP®StatisticsCollege BoardExam QuestionsUnit 1: Exploring One-Variable DataThe Normal Distribution

The Normal Distribution (College Board AP® Statistics)

Exam Questions

5 mins5 questions
1
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In a large data set with a distribution that is approximately normal,

  • a is the value in the data set that has a z-score of 1.00,

  • b is the value of the first quartile, and

  • c is the value of the 10th percentile.

Which of the following is the correct order from least to greatest for the values of a, b, and c?

  • a comma space b comma space c

  • a comma space c comma space b

  • c comma space b comma space a

  • c comma space a comma space b

  • b comma space a comma space c

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2
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The lengths of cat whiskers are approximately normally distributed with a mean of 2.4 inches and a standard deviation of 0.5 inches. Which of the following shaded regions best represents the probability that a randomly selected cat whisker will have a length between 1.4 inches and 2.9 inches?

  • Bell curve representing a normal distribution, highlighting the area between μ - 2σ and μ + σ, with μ as the mean and σ as the standard deviation.
  • Bell curve representing a normal distribution, highlighting the area between μ - 3σ and μ + σ, with μ as the mean and σ as the standard deviation.
  • Bell curve representing a normal distribution, highlighting the area between μ -σ and μ +2σ, with μ as the mean and σ as the standard deviation.
  • Bell curve representing a normal distribution, highlighting the area between μ - 2.9σ and μ - 1.4σ, with μ as the mean and σ as the standard deviation.
  • Bell curve representing a normal distribution, highlighting the area between μ - 2.9σ and μ + 1.4σ, with μ as the mean and σ as the standard deviation.

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3
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The time that a customer spends on hold when calling a helpline is normally distributed with a mean of 7 minutes and a standard deviation of 1.6 minutes. What is the probability that the customer will be on hold for less than 3.8 minutes?

  • 0.025

  • 0.05

  • 0.16

  • 0.95

  • 0.975

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4
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The distribution of weights of adult male koalas is approximately normally distributed, with a mean of 16 pounds and a standard deviation of 0.7 pounds. Two adult male koalas are brought into an animal sanctuary, where they are weighed and named. The first koala, Roger, is at the 47th percentile of the weight distribution. The second koala, Jamie, is 0.19 standard deviations below the mean. At what percentile is Jamie's weight, and how does his weight compare to Roger's?

  • Jamie's weight is at the 58th percentile of the distribution, and he weighs less than Roger.

  • Jamie's weight is at the 42nd percentile of the distribution, and he weighs less than Roger.

  • Jamie's weight is at the 42nd percentile of the distribution, and he weighs more than Roger.

  • Jamie's weight is at the 16th percentile of the distribution, and he weighs less than Roger.

  • Jamie's weight is at the 16th percentile of the distribution, and he weighs more than Roger.

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5
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A set of test scores follows an approximately normal distribution with a mean of 45 and a standard deviation of 5.7. Which of the following equations can be used to find the score x above which 21% of the scores fall?

  • 0.81 equals fraction numerator x minus 45 over denominator 5.7 end fraction

  • 0.79 equals fraction numerator x minus 45 over denominator 5.7 end fraction

  • 0.21 equals fraction numerator x minus 45 over denominator 5.7 end fraction

  • 0.81 equals fraction numerator x minus 45 over denominator open parentheses 5.7 close parentheses squared end fraction

  • 0.79 equals fraction numerator x minus 45 over denominator open parentheses 5.7 close parentheses squared end fraction

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