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US High School Using the Normal Distribution — practice questions

Explore 9 free Using the 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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Using the Normal Distribution questions and exercises with answers

Showing questions 1–9 of 9.

Most z-tables give the area under the normal curve on which side of the z-score?Read the answer and worked solution →To read a probability out of a z-table by hand, what do you work out before opening the table?Read the answer and worked solution →Exam scores are normal with mean 63 and standard deviation 5. The 90th percentile has a z-score of about 1.28. What score is that?Read the answer and worked solution →The area to the left of one z-score is 0.9332 and to the left of another is 0.3446. What area lies between the two?Read the answer and worked solution →Forty percent of the values in a normal distribution are at least k. Which area do you look up to find k?Read the answer and worked solution →Which percentile marks the top of the bottom quartile of a normal distribution?Read the answer and worked solution →To pick out the middle 20 percent of a normal distribution, which two percentiles do you need?Read the answer and worked solution →A normal distribution has a third quartile of 46.3 and a first quartile of 27.5. What is the interquartile range?Read the answer and worked solution →Fill in the percentile recipeRead the answer and worked solution →

Worked practice questions

Most z-tables give the area under the normal curve on which side of the z-score?

  1. The area to its right
  2. The area to its left
  3. The area on both sides
  4. The area at the peak
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Correct answer: B. The area to its left

1. A z-table turns a z-score into an area, and that area is a probability. 2. Most tables report the area lying to the left of the z-score. 3. Any area on the right has to be worked out from that left-hand figure. _Source: OpenStax High School Statistics (CC BY 4.0), Ch 6 "The Normal Distribution", section 6.2 Using the Normal Distribution_

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To read a probability out of a z-table by hand, what do you work out before opening the table?

  1. The median of the data
  2. The range of the data
  3. The mode of the data
  4. The z-score of the value
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Correct answer: D. The z-score of the value

1. A z-table is indexed by z-scores, not by raw data values. 2. So the raw value has to be standardised first. 3. Compute its z-score, then find that z-score in the z-column and read off the area. 4. The median is never needed, since the table already assumes a normal shape. _Source: OpenStax High School Statistics (CC BY 4.0), Ch 6 "The Normal Distribution", section 6.2 Using the Normal Distribution_

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Exam scores are normal with mean 63 and standard deviation 5. The 90th percentile has a z-score of about 1.28. What score is that?

  1. About 56.6 points
  2. About 69.4 points
  3. About 64.3 points
  4. About 76.4 points
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Correct answer: B. About 69.4 points

1. The percentile value equals the mean plus the z-score times the standard deviation. 2. The mean is 63 points and the standard deviation is 5 points. 3. Multiply the z-score by the standard deviation: 1.28 times 5 is 6.4 points. 4. Add that to the mean: 63 plus 6.4 gives 69.4 points. 5. So 90 percent of the scores fall at or below 69.4 points. 6. Answering 56.6 points subtracts the 6.4 and would describe the 10th percentile. 7. Answering 64.3 points adds the z-score itself rather than the z-score times the spread. 8. Answering 76.4 points multiplies by the mean rather than by the standard deviation. _Source: OpenStax High School Statistics (CC BY 4.0), Ch 6 "The Normal Distribution", section 6.2 Using the Normal Distribution_

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More Mathematics topics

Linear InequalitiesSolving Linear EquationsAbsolute Value Equations and InequalitiesMixture and Uniform MotionCompound InequalitiesProblem Solving with EquationsSolving a Formula for a VariableThe Standard Normal Distribution