155S3.4.notebook
January 22, 2010
Section 3­4 Measures of Relative Standing MAT 155­DY1 & DY2
3.4 Measures of Relative Standing 126/2: A sample consists of lengths of American bald eagles, measured in centimeters. If the length of one particular eagle is converted to a z score, what units are used for the z score? Centimeters?
In Course Documents of CourseCompass, see page 10 of S1D.4 MAT 155 Chapters 2 & 3.
Jan 22­7:24 AM
Section 3­4 Measures of Relative Standing 126/4: ZIP codes are arranged from east to west. Eastern states, such as Maine, have ZIP codes beginning with 0, but western states, such as Hawaii, Alaska, and California have ZIP codes beginning with 9. If the first quartile is computed from the list of all ZIP codes, does the result correspond to the location that is 25% of the distance from the location that is farthest east to the location that is farthest west?
Jan 22­7:24 AM
Section 3­4 Measures of Relative Standing 127/8: Sandy Allen is the world’s tallest woman with a height of 91.25 in. (or 7 ft, 7.25 in.). Women have heights with a mean of 63.6 in. and a standard deviation of 2.5 in.
(a) What is the difference between Sandy’s height and the mean height of women?
(b) How many standard deviations is that [answer from part (a)?]
(c) Convert Sandy’s height to a z score.
(d) Does Sandy’s height meet the criterion of being unusual by corresponding to a z score that does not fall between –2 and 2?
Jan 22­7:24 AM
Jan 22­7:24 AM
Section 3­4 Measures of Relative Standing 127/6: Stanford Binet IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.
(a) What is the difference between Einstein’s IQ and the mean?
(b) How many standard deviations is that [answer from part (a)?]
(c) Convert Einstein’s IQ score to a z score.
(d) If we consider “usual” IQ scores to be those that convert to z scores between –2 and 2, is Einstein’s IQ usual or unusual?
Jan 22­7:24 AM
Section 3­4 Measures of Relative Standing 127/10: The Beanstalk Club is limited to women and men who are very tall. The minimum height requirement for women is 70 in. Women’s heights have a mean of 63.6 in. and a standard deviation 2.5 in. Find the z score corresponding to a woman with a height of 70 in. and determine whether that height is unusual.
Jan 22­7:24 AM
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155S3.4.notebook
January 22, 2010
Section 3­4 Measures of Relative Standing 128/12: For men aged between 18 and 24 years, serum cholesterol levels (in mg/100 mL) have a mean of 178.1 and a standard deviation of 40.7 (based on data from the National Health Survey). Find the z score corresponding to a male of that age who has serum cholesterol level of 259.0 mg/100 mL. Is this level unusually high?
Section 3­4 Measures of Relative Standing 128/14: Three students take equivalent stress tests. Which is the highest relative score?
(a) A score of 144 on a test with a mean of 128 and std = 34.
(b) A score of 90 on a test with a mean of 86 and std = 18.
(c) A score of 18 on a test with a mean of 15 and std = 5.
Jan 22­7:24 AM
Section 3­4 Measures of Relative Standing 128/16: Use data of actresses ages from Table 3­4 (page 123) to find the percentile corresponding to age 35.
Jan 22­7:24 AM
Jan 22­7:24 AM
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Section 3­4 Measures of Relative Standing 128/20: Use data of actresses ages from Table 3­4 to find the first quartile.
Jan 22­7:24 AM
Section 3­4 Measures of Relative Standing 128/24: Use data of actresses ages from Table 3­4 to find the 66th percentile.
Jan 22­7:24 AM
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