Chapter 4 – Study Notes

 

1. Probability distributions describe what will __________ happen instead of what actually did happen.

2. What is a random variable?

3. What is a probability distribution?

4. What is the difference between a discrete random variable and a continuous random variable?

5. Looking at Table 4-1 and before looking at Figure 4-3, would you say that the Probability Distribution of the Gender of Children is symmetrical?

6. Read through the examples on Page 182 to help you understand the difference between discrete and continuous random variables.

7. What are the requirements for a Probability Distribution?

8. What are the three ways that a probability distribution can be described?

9. Note the formulas used (4-1 to 4-4) for the various calculations.

10. What is the rule for rounding off numbers?

11. What would be an example where it would be better to not round numbers?

12. According to the range rule of thumb, most values should live within ___ standard deviations of the mean.

13. According to Table 4-2 on page 187, out of 14 births, one would expect the mean number of girls to be ____ and the minimum usual value to be ____ while the maximum usual value would be ____.

14. What probability value is used to determine if results are unusually low or unusually high?

15. What is the expected value?

16. According to the Lottery Numbers Game example, the expected value on a $1 bet is ____.

 

Answer the odd problems on page 190-194.

 

17. What are the four requirements of a binomial probability distribution?

18. Know the notation for Binomial Probability Distribution on page 194-5.

19. What is the rule of thumb for treating events as independent?

20. Work through the 3 methods of calculating binomial probabilities.

 

Answer the odd problems on pages 201-205.

 

21. It would be good to start a reference list of the formulas such as those given on page 205. You will be referring to these formulas throughout the course.

22. According to the example on page 206, is the MicroSort method of gender selection effective?

 

Answer the odd problems on pages 207-210.

 

23. What are some situations where the Poisson Distribution is used?

24. What are the requirements for a Poisson Distribution?

25. What is the standard deviation of the Poisson Distribution?

26. What are the differences between the Poisson and Binomial distributions?

27. Looking at Table 4-4, is there good agreement between the expected number and actual number?

28. Under what conditions can the Poisson distribution be used to approximate the binomial distribution?

 

Answer the odd problems on pages 213 to 215.

 

Do the Review Exercises and Cumulative Review Exercises on pages 217-9.

 

Students enrolled in Math 1442 need to answer the Food for Thought questions on page 215 and (from page 220) calculate the probabilities for a safe flight with a three-engine jet and for a two-engine jet. Write a paragraph that summarizes your findings and the probability of a safe flight. Email your answers to [email protected].

 

The Chapter 4 test will be available starting on ______ until _______. It consists of 19 questions and has a time limit of 40 minutes. You can use your textbook and notes as you take the exam.