Quantitative Reasoning 6C – The Normal Distribution
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State whether you would expect the data set to be normally distributed. \"The amount of property taxes paid by homeowners\"
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Not normal
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State whether you would expect the data set to be normally distributed. \"Times for able bodied female college students to run 400 meters.\"
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Normal
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State whether you would expect the data set to be normally distributed. \"The diameters of the redwood trees in a forest\"
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Normal
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State whether you would expect the data set to be normally distributed. \"Sales of birthday cards over a one-year period\"
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Not normal
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For women at Hartford College, times to run 400 meters are normally distributed with a mean of 84 seconds and a standard deviation of 7 seconds. What percentage of the times are more than 63 seconds?
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99.85%
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Scores on a test are normally distributed with a mean of 102 and a standard deviation of 16. What percentage of scores are greater than 134?
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2.5%
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At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.5 and 3.3?
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68%
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The amount of Jen's monthly phone bill is normally distributed with a mean of $53 and a standard deviation of $11. What percentage of her phone bills are between $20 and $86?
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99.7%
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Assume that a distribution has a mean of 21 and a standard deviation of 6. What percentage of the values in the distribution do we expect to fall between 15 and 21?
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34%
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Assume that a distribution has a mean of 24 and a standard deviation of 6. What percentage of the values in the distribution do we expect to fall between 24 and 36?
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47.5%
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For adults in the town of Bridgeport, systolic blood pressure is normally distributed with a mean of 140 mmHg and a standard deviation of 10 mmHg. What percentage of adults in the town have a systolic blood pressure less than 110 mmHg?
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0.15%
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The amount of Jen's monthly phone bill is normally distributed with a mean of $56 and a standard deviation of $12. 68% of her phone bills are between $_____ and $______.
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$44 and $68
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The annual precipitation for one city is normally distributed with a mean of 30.6 inches and a standard deviation of 3.1 inches. In 99.7% of the years, the precipitation in this city is between _______ and _______ inches.
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21.3 and 39.9
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Scores on a test are normally distributed with a mean of 102 and a standard deviation of 7. What is the standard score for an exam score of 108?
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0.86
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Scores on a test are normally distributed with a mean of 112 and a standard deviation of 13. What is the exam score corresponding to a standard score of -0.67?
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103.29
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For the data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
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z = 0.6, percentile = 72.57
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For the data value, find the standard score and the percentile. A data value 1.3 standard deviations above the mean.
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z = 1.3, percentile = 90.32
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For the data value, find the standard score and the percentile. A data value 0.9 standard deviations below the mean.
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z = -0.9, percentile = 18.41
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For the data value, find the standard score and the percentile. A data value 2.3 standard deviations below the mean.
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z = -2.3, percentile = 1.07
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Find the standard score for the given data value. A data value in the 8th percentile.
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z = -1.4
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Find the standard score for the given data value. A data value in the 31st percentile.
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z = -0.5
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Find the standard score for the given data value. A data value in the 58th percentile.
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z - 0.2
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Find the standard score for the given data value. A data value in the 97th percentile.
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z = 1.9
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Suppose that the mean salary in a particular profession is $45,000 with a standard deviation of $2,000. To what percentile does a salary of $48,000 correspond?
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93rd
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Scores on a test are normally distributed with a mean of 70 and a standard deviation of 5. What is the percentile for an exam score of 61? Round to the nearest tenth.
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78.8
