Math 3118, Section 1
Fall 2002
Review questions for the 4^th test

1. In the ABC corporation, the salaries are as follows:
   • 100 people earn $20,000 per year
   • 20 people earn $40,000 per year
   • 2 people earn $100,000 per year
   • 1 person earns $1,000,000 per year
      
   1. Determine the mean salary and the median salary
   2. Which of these two central measures is more representative of the "typical worker's" salary? Please comment.
       
2. On a test , where the possible scores were from 1 to 9, the following numbers of people received each score:
     

   Score	0	1	2	3	4	5	6	7	8	9
   frequency	0	0	5	10	15	25	30	20	15	5

   1. Find the median, mean and standard deviation.
   2. Plot the frequency as a function of the score.
      It's OK just to make dots, similarly to Figure 11.1 in the text.
      (Of course, it will be scaled differently . . . )
         
3. =Exercise 11.2.15 in the text
     
4. A fair coin is flipped 100 times
   1. Determine the expected number of heads.
   2. Determine the standard deviation for this experiment.
   3. Find the probability that the number of heads will be:
   • 60 or greater
   • 45 or fewer
   • between 45 and 55 (inclusive)
       
5. The scores of students on a standardized test are normally distributed, with a maximum possible score of 1000, a mean of 700 and a standard deviation of 90.
   Find the z-values and also the actual scores corresponding to each of the following:
   1. The score above which 85% of the scores are situated.
   2. The score below which 95% of the scores are situated.
   3. The z-value such that 80% of the normal curve lies within z standard deviation units of the mean, and the actual scores (at equal distance and opposite directions from the mean) such that 80% of the students have scores between these two scores.
        
6. Calculate the following:
   
   1. 
       
   2. 
       
   3. 
       
   4. 
       
        
7. A car worth $15,000 is the first prize in a raffle, along with 2 second prizes worth $500 each and 10 third prizes worth $75 each.
   A ticket costs $2, and 20,000 tickets are sold. The tickets are thoroughly mixed, so that all tickets are equally likely to be drawn.
   Winning tickets are removed from the drawing for further prizes. [Given the large number of tickets, this may not significantly change the result. In particular, the probability of a ticket being drawn on the second round changes from  ¹/_20,000  to  ¹/_19,999 . But neglecting to make that change may not seriously affect the accuracy of your answer.]
    
   Determine the expected net winnings of a person who buys 1 ticket. Remember to take the price of the ticket into account.
    
    
8. Review the class exercises and homework problems.