Math 3118, Section 3

Spring 2001

Thursday, April 26 class handout

Class exercises

1. Exercises from the text:

 
• Exercise 11.4.2
• Exercise 11.4.3
• Exercise 11.4.4
• Exercise 11.4.6
• Exercise 11.4.7
   
2. Supplementary exercise #1
   • One thousand left handed students and one thousand right handed students took a test. For the left handed students, the mean score was 75, and for the right handed students the mean score was 72.
      
   • Assume that the standard deviation was 4 points for the left-handed students and 6 points for the right-handed students. Determine how many left-handed students and how many right-handed 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 left-handed 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??)
      

 

Homework due Tuesday, May 1

1. Supplementary exercise #2
   • As in supplementary exercise #1, we again consider a situation where one thousand left handed students and one thousand right handed students took a test. As before, the mean score for the left handed students was 75, and for the right handed students the mean score was 72.
      
   • This time, however, we assume that the standard deviation was 8 points for the left-handed students and 4 points for the right-handed students. Determine how many left-handed students and how many right-handed 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 "left-handed students usually scored higher than right-handed students".
     (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. (For instance, the differences might be more noticeable toward one or the other end of the scale.)
      
3. = Exercise 11.4.1 from the text
    
4. = Exercise 11.4.5 from the text
   Note:In this exercise, the phrase "within  z standard deviation units of the mean" indicates that we are looking for a region that includes areas on  both sides of the mean. After finding the value of  A(z) ¿¿what else do we have to do in order to find the desired area??