Graded Review 1 Answers (Normal Curve Problems)

A team of educational psychologists and special education teachers developed Panukat ng Mga Kakayahang Di-Berbal (PKDB), a test specially designed to measure nonverbal abilities of Filipino students with learning disabilities (FSLD). During the development of the instrument, it was established that PKDB scores approximate a normal distribution with a mean of 63 and a standard deviation of 20. (Lower scores indicate delay in the development of nonverbal abilities)

Using the given information above, determine the correct/best answer for each of the problems below.

Click HERE if you wish to use an online calculator.

Click HERE to view a normal curve table.

1. What is the z-score equivalent of the raw score 63 in PKDB?
   
   
   1. 1197
      
   2. 0.00
      
   3. 0.50
      
   4. 1323
   5. No Answer. The correct answer is _________.


2. What proportion of FSLD can be expected to score below 63?
   
   
   1. 50.00
      
   2. 0.00
      
   3. 1.00
      
   4. 0.50
   5. No Answer. The correct answer is _________.


3. What percentage of FSLD can be expected to score above 63?
   
   
   1. 0.50
      
   2. 0.00
      
   3. 50.00
      
   4. 100.00
   5. No Answer. The correct answer is _________.


4. What is the z-score equivalent of the raw score 70 in PKDB?
   
   
   1. 0.35
      
   2. 1470
      
   3. 1330
      
   4. -0.35
   5. No Answer. The correct answer is _________.


5. What is the area under the normal curve between the mean and your answer in the previous item?
   
   
   1. 0.1368
      
   2. 0.3632
      
   3. 0.6368
      
   4. 0.8632
   5. No Answer. The correct answer is _________.


6. What proportion of FSLD can be expected to have scores above 70?
   
   
   1. 0.1368
      
   2. 0.3632
      
   3. 0.6368
      
   4. 0.8632
   5. No Answer. The correct answer is _________.


7. Suppose 164 FSLD were randomly sampled to take PKDB. How many can be expected to have scores above 70?
   
   
   1. 104
      
   2. 22
      
   3. 60
      
   4. 142
   5. No Answer. The correct answer is _________.


8. What is the z-score equivalent of the raw score 92 in PKDB?
   
   
   1. 1903
      
   2. -1777
      
   3. -1.45
      
   4. 1.45
   5. No Answer. The correct answer is _________.


9. What is the area under the normal curve between the mean and and your answer in the previous item?
   
   
   1. 0.9625
      
   2. 0.4265
      
   3. 0.0735
      
   4. 0.5735
   5. No Answer. The correct answer is _________.


10. What percentage of FSLD can be expected to have scores below 92?
    
    
    1. 92.65
       
    2. 42.65
       
    3. 57.35
       
    4. 7.35
    5. No Answer. The correct answer is _________.


11. What is the z-score equivalent of the raw score 50 in PKDB?
    
    
    1. 0.65
       
    2. -937
       
    3. -0.65
       
    4. 1063
    5. No Answer. The correct answer is _________.


12. What is the area under the normal curve between the mean and and your answer in the previous item?
    
    
    1. 0.2578
       
    2. 0.2422
       
    3. 0.7422
       
    4. 0.7578
    5. No Answer. The correct answer is _________.


13. What is the proportion of FSLD that can be expected to have scores below 50?
    
    
    1. 0.2422
       
    2. 0.2578
       
    3. 0.7578
       
    4. 0.7422
    5. No Answer. The correct answer is _________.


14. What is the z-score equivalent of the raw score 38 in PKDB?
    
    
    1. 1.25
       
    2. 823
       
    3. -697
       
    4. -1.25
    5. No Answer. The correct answer is _________.


15. What is the area under the normal curve between the mean and and your answer in the previous item?
    
    
    1. 0.8944
       
    2. 0.3944
       
    3. 0.1056
       
    4. 0.6056
    5. No Answer. The correct answer is _________.


16. What percentage of FSLD can be expected to have scores above 38?
    
    
    1. 10.56
       
    2. 39.44
       
    3. 60.56
       
    4. 89.44
    5. No Answer. The correct answer is _________.


17. What is the z-score equivalent of the raw score 40 in PKDB?
    
    
    1. -1.15
       
    2. 1.15
       
    3. 863
       
    4. -737
    5. No Answer. The correct answer is _________.


18. What is the area under the normal curve between the mean and your answer in the previous item?
    
    
    1. 0.6251
       
    2. 0.3749
       
    3. 0.8749
       
    4. 0.1251
    5. No Answer. The correct answer is _________.


19. What is the z-score equivalent of the raw score 60 in PKDB?
    
    
    1. 1263
       
    2. -0.15
       
    3. 0.15
       
    4. 1137
    5. No Answer. The correct answer is _________.


20. What is the area under the normal curve between the mean and and your answer in the previous item?
    
    
    1. 0.4404
    2. 0.5596
    3. 0.0596
    4. 0.9404
       
    5. No Answer. The correct answer is _________.


21. What proportion of FSLD can be expected to have PDKB scores between 40 and 60?
    
    
    1. 0.4345
    2. 0.3153
    3. 0.5655
    4. 0.6847
    5. No Answer. The correct answer is _________.


22. Suppose 378 randomly selected test takers took PKDB. How many can be expected to have scores between 40 and 50?
    
    
    1. 164
    2. 214
    3. 119
    4. 259
       
    5. No Answer. The correct answer is _________.


23. What is the z-score equivalent of the raw score 36?
    
    
    1. 783
       
    2. -675
       
    3. -1.35
       
    4. 1.35
    5. No Answer. The correct answer is _________.


24. What is the area under the normal curve between the mean and and your answer in the previous item?
    
    
    1. 0.4115
       
    2. 0.0885
       
    3. 0.9115
       
    4. 0.5885
    5. No Answer. The correct answer is _________.


25. What is the z-score equivalent of the raw score 94?
    
    
    1. 1.55
       
    2. 1943
       
    3. -1817
       
    4. -1.55
    5. No Answer. The correct answer is _________.
       


26. What is the area under the normal curve between the mean and and your answer in the previous item?
    
    
    1. 0.5606
       
    2. 0.9394
    3. 0.0606
       
    4. 0.4394
       
    5. No Answer. The correct answer is _________.
       


27. What percentage of FSLD can be expected to have PKDB scores between 36 and 94?
    
    
    1. 47.21
       
    2. 97.21
       
    3. 2.79
       
    4. 14.91
    5. 85.09
    6. 52.79
    7. No Answer. The correct answer is _________.


28. What z-score has an area of 0.2190 from the mean?
    
    I. 0.33
    II. -0.33
    
    
    1. I alone
       
    2. II alone
       
    3. both I and II
       
    4. neither I nor II
       


29. What scores serve as boundaries for the middle 43.80% of FSLD's scores in PKDB?
    
    
    1. 59.4 and 66.6
       
    2. 51.4 and 74.6
       
    3. 47.4 and 78.6
       
    4. 33.4 and 92.6
    5. No Answer. The correct answer is _________.


30. What z-score/s has/have an area of 0.1400 from the mean?
    
    
    1. -1.08
       
    2. 0.36
       
    3. -0.36
       
    4. -0.36 and 0.36
    5. -1.08 and 1.08
    6. 1.08
    7. No Answer. The correct answer is _________.


31. What z-score/s has/have an area of 0.1400 below it?
    
    
    1. -1.08
       
    2. 0.36
       
    3. -0.36
       
    4. -0.36 and 0.36
    5. -1.08 and 1.08
    6. 1.08
    7. No Answer. The correct answer is _________.
    
    
32. What PKDB score separates the 14% of FSLD with the most developed nonverbal abilities from the rest?
    
    
    1. 41.40
       
    2. 84.60
       
    3. 70.20
       
    4. 55.80
    5. No Answer. The correct answer is _________.


33. Suppose 87 out of 400 randomly selected students with learning disability were classified as having severely delayed nonverbal abilities. What PKDB score must one have to be classified as severely delayed?
    
    
    1. below 78.60
    2. above 78.60
       
    3. below 47.40
       
    4. above 47.40
    5. above 51.40
       
    6. below 51.40
    7. above 74.60
    8. below 74.60
    9. No Answer. The correct answer is _________.


34. What z-score must be used to correctly answer item 33?
    
    
    1. 0.78
       
    2. 0.58
       
    3. -0.58
       
    4. -0.78
    5. No Answer. The correct answer is _________.