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US High School The Standard Normal Distribution — practice questions

Explore 2 free The Standard Normal Distribution questions in US High School Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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The Standard Normal Distribution questions and exercises with answers

Showing questions 1–2 of 2.

A reading test is normal with mean 70 and standard deviation 8. Which z-score belongs to a mark of 86?Read the answer and worked solution →A normal distribution has mean 50 and standard deviation 6. Which value carries a z-score of negative 1.5?Read the answer and worked solution →

Worked practice questions

A reading test is normal with mean 70 and standard deviation 8. Which z-score belongs to a mark of 86?

  1. The z-score is 2
  2. The z-score is 8
  3. The z-score is 16
  4. The z-score is 4
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Correct answer: A. The z-score is 2

1. The mark sits above the mean, so the z-score will be positive. 2. Subtract the mean from the mark: 86 minus 70 is 16. 3. Divide that gap by the standard deviation of 8. 4. That gives a z-score of 2. 5. Answering 16 stops at the raw gap and never converts it into standard deviations. _Source: OpenStax High School Statistics (CC BY 4.0), Ch 6 "The Normal Distribution", section 6.1 The Standard Normal Distribution_

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A normal distribution has mean 50 and standard deviation 6. Which value carries a z-score of negative 1.5?

  1. The value is 59
  2. The value is 44
  3. The value is 41
  4. The value is 35
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Correct answer: C. The value is 41

1. Rearranged, the value equals the mean plus the z-score times the standard deviation. 2. Here that is 50 plus negative 1.5 times 6. 3. Negative 1.5 times 6 is negative 9. 4. So the value is 50 minus 9, which is 41. 5. Answering 59 adds the 9 instead of subtracting it and lands above the mean. _Source: OpenStax High School Statistics (CC BY 4.0), Ch 6 "The Normal Distribution", section 6.1 The Standard Normal Distribution_

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