Download Review Worksheet - Statistics and Data Analysis

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REVIEW SHEET #2
DISCRIBING DATA
Stem and Leaf Plot: Page 65 #11
5 Number Summary: Page 89 #3, #7
Box Plot: page 91: #19 & #13 (make a boxplot of the data before answering)
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PROBABILITY
Page 334 #13, 23, 29
Page 356 #3, 9, 43
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NORMAL DISTRIBUTION
1) A set of mathematics exam scores has a mean of 70 and a standard deviation of 8. A set of English exam
scores has a mean of 74 and a standard deviation of 16. For which exam would a score of 78 have a higher
standing?
2) For a distribution of raw scores with a mean of 45, the Z-score for a raw score of 55 is calculated to be -2.00.
Regardless of the value of the standard deviation, why must this Z-score be incorrect?
3) In a population of scores a raw score with the value of 83 corresponds to a Z of +1.00 and a raw score of 86
corresponds to a Z of +2.00. What is the mean and standard deviation of this population?
4) On a statistics exam, you have a score of 73. If the mean of the exam is 65 would you prefer the standard
deviation of the scores to be 8 or 16? Why?
5) A normal distribution has a mean of 120 and a standard deviation of 20. For this distribution
a. What score separates the top 40% of the scores from the rest?
b. What score corresponds to the 90th percentile?
6. The heights of 15 year old American males are approximately normally distributed with mean 170 cm and
standard deviation 7.6 cm. What proportion of these young men have heights greater than 185 cm?
7. The maximum oxygen uptake of middle-aged American men is approximately normally distributed with
mean 42.2 mL/kg/min and standard deviation 3.7 mL/kg/min.
(a) What proportion of middle-aged men have maximum oxygen uptake levels lower than 35 mL/kg/min?
(b) Higher levels of maximum oxygen uptake are indicative of better health. What level would put a midle-aged
man in the top 5% of healthy individuals?
8. Most measures of IQ are normally distributed, and scaled to have mean 100 and standard deviation 15.
(a) What percentage of people will have IQs that are lower than 88?
(b) The organization MENSA only accepts members who score in the top 2% of IQ tests. What range of scores
would enable one to join MENSA?
(c) People who score in the lowest 10% of IQ scores are often eligible for additional services in school. What
range of IQ scores would enable a student to receive special services?
9. A given distribution has a mean of 50. A score of 43 has a corresponding z-score of -l.94. What is the
standard deviation (to the nearest hundredth)?
10. Given a normal distribution with a mean of 80 and a standard deviation of 5, we know that approximately
what percent of the values are between 70 and 90?
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ANSWERS
Normal
1.
2.
3.
4.
5.
6.
7.
Math
Score is above the mean
Mean = 80; standard deviation = 3.0
8 because that puts you an entire standard deviation above the mean
A) 125 b) 145.60
2.44
A) 2.62%
B) Z=1.65% X=48.305
8. A) 78.81%
B) X=130.75
9. 3.61
10. 95%
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