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Praxis Core (Teaching) The Normal Distribution — practice questions

Explore 26 free The Normal Distribution questions in Praxis Core (Teaching) Mathematics. 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 1–26 of 26.

A normal curve is symmetric about a vertical line drawn through which value?Read the answer and worked solution →In a normal distribution, where do the mean, the median and the mode sit?Read the answer and worked solution →The standard normal distribution has which mean and standard deviation?Read the answer and worked solution →A z-score reports how far a value sits from the mean, measured in which units?Read the answer and worked solution →A value that is smaller than the mean of its distribution has which kind of z-score?Read the answer and worked solution →What does a z-score of exactly zero tell you about a value?Read the answer and worked solution →In a normal distribution, about what percent of values lie within one standard deviation of the mean?Read the answer and worked solution →The total area under a normal curve always adds up to what number?Read the answer and worked solution →The graph of a normal distribution has which overall shape?Read the answer and worked solution →Two normal curves share the same mean, but one has a larger standard deviation. How does that one look?Read the answer and worked solution →Changing only the mean of a normal distribution does what to its graph?Read the answer and worked solution →About 99.7 percent of the values of a normal distribution fall within how many standard deviations of the mean?Read the answer and worked solution →Why can a z-score compare a score from one test with a score from a completely different test?Read the answer and worked solution →A normal distribution has a mean of 50 and a standard deviation of 6. About 68 percent of its values lie between which two numbers?Read the answer and worked solution →A normal distribution has a mean of 50 and a standard deviation of 6. About 95 percent of its values lie between which two numbers?Read the answer and worked solution →The area to the left of a value on a normal curve is 0.0228. What is the area to its right?Read the answer and worked solution →On a final exam, 39 percent of students scored less than 75. What percent scored higher than 75?Read the answer and worked solution →A test score sits at the 90th percentile. What does that position mean?Read the answer and worked solution →A doctor reports that a patient's blood pressure has a z-score of 1.75. Which reading is correct?Read the answer and worked solution →In a sample of 100 cars the number of faulty cars has a mean of 10 and a standard deviation of 3. About 68 percent of samples hold how many faulty cars?Read the answer and worked solution →A coin is flipped 100 times. The number of heads has a mean of 20 and a standard deviation of 4. About 95 percent of the time the head count lands where?Read the answer and worked solution →Line up three tiles that agreeRead the answer and worked solution →Drop each trait into the right curveRead the answer and worked solution →Knock out the z-score mythsRead the answer and worked solution →Swipe each z-score to its sideRead the answer and worked solution →Walk the z-scale left to rightRead the answer and worked solution →

Worked practice questions

A normal curve is symmetric about a vertical line drawn through which value?

  1. The mean
  2. The range
  3. The count
  4. The total
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Correct answer: A. The mean

1. A normal curve has one hump and two tails that fall away evenly. 2. The line of symmetry runs vertically through the mean. 3. Fold the picture along that line and the two halves match. _Source: OpenStax High School Statistics (CC BY 4.0), section 6.1 The Standard Normal Distribution_

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In a normal distribution, where do the mean, the median and the mode sit?

  1. All at different points
  2. All at the same point
  3. All at the left tail
  4. All at the right tail
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Correct answer: B. All at the same point

1. The mean is the balance point, the median splits the data in half, and the mode is the peak. 2. A normal curve is symmetric, so its balance point and its halfway point are the same place. 3. That same place is also the highest point of the curve, so all three land together. _Source: OpenStax High School Statistics (CC BY 4.0), section 6.1 The Standard Normal Distribution_

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The standard normal distribution has which mean and standard deviation?

  1. Mean 1, standard deviation 0
  2. Mean 0, standard deviation 0
  3. Mean 0, standard deviation 1
  4. Mean 1, standard deviation 1
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Correct answer: C. Mean 0, standard deviation 1

1. The standard normal is the one special curve every other normal can be turned into. 2. Its mean is set at 0, so the centre of the curve sits at zero. 3. Its standard deviation is set at 1, so one step out from the centre is one unit. 4. A standard deviation of 0 would mean no spread at all, which is not a curve. _Source: OpenStax High School Statistics (CC BY 4.0), section 6.1 The Standard Normal Distribution_

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