Math 3118, Section 1
Fall 2002
Wednesday, December 4 class handout

1. Exercises from the text:
    
   • Exercise 11.4.7
      
   • Exercise 11.4.8
     For suggestions, see Information about the normal curve, Part IA
      
2. Supplementary exercise #1
   • One thousand students from School District M and one thousand students from School District S took a test. For the students from District M, the mean score was 75, and for the students from District S the mean score was 72.
      
   • Assume that the standard deviation was 4 points for the District M students and 6 points for the District S students. Determine how many District M students and how many District S students had scores:
     1. 80 or above
     2. 85 or above
     3. 90 or above
     4. 70 or below
     5. 65 or below
     6. 60 or below
     
      
     Suggestions: As in the exercises in the text, you need to subtract the mean from the score in question (after shifting appropriately by 1/2) and then divide by the standard deviation in order to get the z-value.
     For instance: If we're considering District M students, then for scores of 80 or above we subtract the mean (=75) from 79.5 to get a difference of 4.5 points. To find the z-value, we divide this difference by the standard deviation (=4), obtaining 1.125 standard deviation units. Thus, z is about 1.1.
     Now, A(z) gives the area under the normal curve between 0 and z. We need the area under the curve which is to the right of z, so we take note of the fact that the total area under the right half of the normal curve is .5 and proceed accordingly. (¿¿Should we add or subtract??)   The figure and discussion in Information about the normal curve, Part IA is relevent to this situation.
      
      
3. Further exercises from the text
    
   • Exercise 11.5.2
      
   • Exercise 11.5.3
      
   • Exercise 11.5.4
      

Homework due Monday, December 9

1. Supplementary exercise #2
   • One year later, one thousand students from School District M and one thousand students from School District S took another standardized test. This time, the mean score for the students from District M was 72, with a standard deviation of 4. For the students from District S the mean score was 75, with a standard deviation of 6.
      
   • Determine how many District M students and how many District S students had scores:
     1. 80 or above
     2. 85 or above
     3. 90 or above
     4. 70 or below
     5. 65 or below
     6. 60 or below
     
      
     Similar suggestions apply, as in supplementary exercise 1 above.
   
    
2. Supplementary exercise #3
   • Comment on the statement that "students from our district scored higher than students from the other district". (A similar question is asked in exercise 11.3.2 in the text.) Use information from the supplementary class and homework exercises to illustrate your answers.
      
   • In particular, discuss how the answers on the homework exercise were different from the answers on the class exercise -- including not only the obvious fact that the means have become switched. (For instance, the differences toward one or the other end of the scale might not quite be what the difference in means would lead us to expect.) Also, discuss any aspects in which the comparisons may not have changed so dramatically.
      
3. §11.5 #5