Intro to Statistics for the Social Sciences Fall 2014, Dr. Suzanne Delaney
Homework #11
This homework will provide practice in finding and manipulating means, raw scores, z scores and probabilities using the normal curve. We will assume a normal curve for these problems, and will use the z-table provided here on last page. Please show your work (write small and neat) and circle your final answer.
For questions 1 - 15 please assume a distribution with a mean of 30 and a standard deviation of 2. 1. Find the area under the curve between scores of 28 – 32.
Start by filling in the desired information on curve 1 (to the right)
(Note this one doesn’t require calculations – just those “empirical rules we memorized for class)
2. Find the area under the curve between scores of 26 – 34. Start by filling in the desired information on curve 2 (to the right)
(Note this one doesn’t require calculations – just those “empirical rules we memorized for class)
3. Find the area under the curve between scores of 24 – 36. Start by filling in the desired information on curve 3 (to the right)
(Note this one doesn’t require calculations – just those “empirical rules we memorized for class)
4. Find the area under the curve for scores of 30 and above. Start by filling in the desired information on curve 4 (to the right) (Note this one doesn’t require calculations)
5. Find the area under the curve between scores of 30 – 33. Start by filling in the desired information on curve 5 (to the right)
(Note this one will require you to calculate a z-score for a raw score of 33 and use the z-table)
6. Find the area under the curve associated with a score of 33 and below. Start by filling in the desired information on curve 6 (to the right).
(Note this one will require you to calculate a z-score for a raw score of 33 and use the z-table) Fun fact, in this problem you are finding the percentile rank for a score of 33
7. Find the area under the curve associated with a score of 33 and above. Start by filling in the desired information on curve 7 (to the right).
1 3 2 4 5 6 7 Lab Session: _____ CID Number: _________ Name: _____________________________
8. Find the area under the curve associated with a score of 29 and above. Start by filling in the desired information on curve 8 (to the right). 9. Find the area under the curve between scores of 25 – 31.
Start by filling in the desired information on curve 9 (to the right) (Note this one will require you to calculate a z-score for the raw scores of 25 and 31)
10. Find the percentile rank for a score of 27. Start by filling in the desired information on curve 10 (to the right). Hint: this is similar to problem 6
(Note this one will require you to calculate a z-score for a raw score of 27 and use the z-table)
11. Find the area under the curve associated with a score of 25 and above. Start by filling in the desired information on curve 11 (to the right).
12. Find the area under the curve associated with a score of 32 and above. Start by filling in the desired information on curve 12 (to the right).
13. Find the raw score that is associated with the 50th percentile
(Note: no calculations are necessary)
14. Find the 2 raw scores associated with the middle 68 percent of the curve
(Note: no calculations are necessary)
15. Find the raw score that is the 77th percentile (Note this one will require you to find a z-score from the area under the curve - by using the z-table backwards)
Remember, raw score = mean + (z score)(standard deviation)
16. Find the raw score that is the 13th percentile (Note this one will require you to find a z-score from the area under the curve - by using the z-table backwards)
Remember, raw score = mean + (z score)(standard deviation)
8 9 10 11 12 14 15 13 16
For questions 17 - 32 please use the following distribution with a mean of 200 and a standard deviation of 40.
17. Find the area under the curve between scores of 160 – 240. Start by filling in the desired information on curve 17 (to the right)
(Note this one doesn’t require calculations – just those “empirical rules we memorized for class)
18. Find the area under the curve between scores of 120 – 280. Start by filling in the desired information on curve 18 (to the right)
19. Find the area under the curve between scores of 80 – 320. Start by filling in the desired information on curve 19 (to the right)
(Note this one doesn’t require calculations – just those “empirical rules we memorized for class)
20. Find the area under the curve between scores of 200 and 230. Start by filling in the desired information on curve 20 (to the right)
(Note this one will require you to calculate a z-score for a raw score of 230 and use the z-table)
21. Find the area under the curve associated with a score of 190 and below. Start by filling in the desired information on curve 21 (to the right).
(Note this one will require you to calculate a z-score for a raw score of 190 and use the z-table) Fun fact, in this problem you are finding the percentile rank for a score of 190
22. Find the area under the curve associated with a score of 180 and above. Start by filling in the desired information on curve 22 (to the right).
23. Find the area under the curve associated with a score of 236 and above. Start by filling in the desired information on curve 23 (to the right).
24. Find the area under the curve between scores of 192 – 222. Start by filling in the desired information on curve 24 (to the right) (Note this one will require you to calculate a z-score for the raw scores of 192 and 222)
22 23 24 20 19 18 17 21
25. Find the percentile rank for a score of 275. Start by filling in the desired information on curve 25 (to the right).
(Note this one will require you to calculate a z-score for a raw score of 275 and use the z-table) Hint: this is similar to problem 18
26. Find the area under the curve associated with a score of 295 and above. Start by filling in the desired information on curve 26 (to the right).
27. Find the area under the curve associated with a score of 130 and above. Start by filling in the desired information on curve 27 (to the right).
28. Find the area under the curve associated with a score of 130 and below. Start by filling in the desired information on curve 28 (to the right).
29a. Find the raw score that is the 99th percentile (Hint: Similar to problem 15) Remember, raw score = mean + (z score)(standard deviation)
29b. Find the raw score that marks the 33rd percentile
Remember, raw score = mean + (z score)(standard deviation)
31. Find the raw score that marks the 40th percentile
Remember, raw score = mean + (z score)(standard deviation)
32. Find the raw score that marks the 67th percentile
Remember, raw score = mean + (z score)(standard deviation)
25 26 27 28 29 31 30 32
