Review 1 Answers (Normal Curve Problems)

Ms Mavie Lees administered a test of psychomotor speed to her 42 SpEd students. She found out that the time (in minutes) it took her students to finish the test was normally distributed with an average of 70.5 minutes and a standard deviation of 2.662 minutes.

PART I.

If the required answer is...	Then, round it off to the nearest...
- proportion, - percentage, - number of students,	- four decimal places - two decimal places - whole number

1. What proportion of students finished the test in less than 70.5 minutes?
   0.5000
   
   
2. How many students finished the test in less than 70.5 minutes?
   21 students
   
   
3. What percentage of students needed more than 70.5 minutes to finish the test?
   50.00%
   
   
4. How many students needed more than 70.5 minutes to finish the test?
   21 students
   
   
5. What proportion of students completed the test in less than 71.5 minutes?
   0.6480
   
   
6. How many students completed the test in less than 71.5 minutes?
   27 students
   
   
7. What percentage of students required more than 68.5 minutes to finish the test?
   77.34%
   
   
8. How many students required more than 68.5 minutes to finish the test?
   32 students
   
   
9. What proportion of students needed less than 69.5 minutes to finish the test?
   0.3520
   
   
10. How many students needed less than 69.5 minutes to finish the test?
    15 students
    
    
11. What percentage of students had to work for more than 72.5 minutes to complete the test?
    22.66%
    
    
12. How many students had to work for more than 72.5 minutes to complete the test?
    10 students
    
    
13. What proportion of students needed between 66.5 and 71.5 minutes to finish the test?
    0.5812
    
    
14. How many students needed between 66.5 and 71.5 minutes to finish the test?
    12 students
    
    
15. What percentage of students finished the test within 72.5 and 74.5 minutes?
    15.98%
    
    
16. How many students finished the test within 72.5 and 74.5 minutes?
    7 students
    
    
17. What proportion of students finished the test within 67.5 and 68.5 minutes?
    0.0974
    
    
18. How many students finished the test within 67.5 and 68.5 minutes?
    4 students
    

PART II.

Round off your answer to 2 decimal places.

For questions 1-8, your answer should also include either the words “or shorter” or “or longer.” For example, “25.75 minutes or shorter” or “25.75 minutes or longer.”


To finish the test, how much time was needed by the...

1. … fastest 14% of the students?
   67.63 minutes of shorter
   
   
2. … fastest 10 students?
   68.61 minutes or shorter
   
   
3. … fastest 64% of the students?
   71.46 minutes or shorter
   
   
4. … fastest 36 students?
   73.35 minutes or shorter
   
   
5. … slowest 6 students?
   73.35 minutes or longer
   
   
6. … slowest 24% of the students?
   72.39 minutes or longer
   
   
7. … slowest 39 students?
   66.59 minutes or longer
   
   
8. … slowest 64% of the students?
   69.54 minutes or longer
   
   
9. … middle 85% of the students?
   66.67 to 74.33 minutes
   
   
10. … middle 52% of the students?
    68.61 to 72.39 minutes