Ms. Rigano's Math Classes
Practice – a little Harder… Name:
1. 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?
c. What range of scores would form the middle 60% of this distribution?
2. A patient recently diagnosed with Alzheimer's disease takes a cognitive abilities test. The patient scores a 45 on the test (mean = 52, standard deviation of 5. What is this patient's percentile rank?
3. Another patient with Parkinson's disease takes the same cognitive abilities test as in the question above and scores a 54. What percent of individuals would receive higher score?
4. A fifth grader takes a standardized achievement test (mean = 125, S = 15) and scores a 148. What is this child's percentile rank?
5. Pat and Chris both took a spatial abilities test (mean = 80, S = 8). Pat scored a 76 and Chris scored a 94. What percent of individuals would score between Pat and Chris?
6. If we know that the standard deviation of the population is 5.8, then what is the variance?
7. 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?
8. 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?
9. 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?
10. 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?
11. The given data set is comprised of 4067 measurements that represent a normal distribution and a mean of 850. If 68% of the data lies between 795 and 905 then what is the standard deviation?
12. In a college class, a test score of 86 corresponds to a Z of +1.00 and a test score of 76 corresponds to a Z of +.38. What is the mean and standard deviation of test?
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