binomial distribution.pptx additional mathematics

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1. 5.2 BINOMIAL DISTRIBUTION

2. QUIZ RECALL WHAT WAS LEARNED IN THE PREVIOUS LESSON

3. The number of arrivals at an emergency room between midnight and  6:00a.m The air pressure of a tire on an automobile. The duration of the next outgoing telephone call from a business office. The number of kernels of popcorn in a  11 -pound container. The number of applicants for a job The number of boys in a randomly selected three-child family The temperature of a cup of coffee served at a restaurant. The amount of rain recorded at an airport one day. The number of vehicles owned by a randomly selected household The distance a rental car rented on a daily rate is driven each day.

4. BERNOULLI TRIALS An experiment that produces only two possible outcomes

5. CHARACTERISTICS

6. EXAMPLE

7. BINOMIAL DISTRIBUTION

8. Application in Real Life

9. MEDICAL FIELD Medical professionals use the binomial distribution to model the probability that a certain number of patients will experience side effects as a result of taking new medications.

10. BANKING AND FINANCE Banks use the binomial distribution to model the probability that a certain number of credit card transactions are fraudulent

11. Shopping Returns per Week Retail stores use the binomial distribution to model the probability that they receive a certain number of shopping returns each week.

12. RECONISING BINOMIAL DISTRIBUTION

13. The diagram on the right shows a tree diagram of all the possible outcomes after two rounds of tic-tac-toe game. Is this a binomial distribution? Explain.

14. A shelf contains 6 identical copies of chemistry reference books and 4 identical copies of physics reference books. 3 copies of the physics reference books are taken at random from the shelf one after another without replacement. State whether this probability distribution is a binomial distribution or not. Explain.

15. In a survey, it is found that 9 out of 10 students from a certain college have part-time jobs. If 4 students are randomly selected from that college, is the probability distribution for students doing part time jobs binomially distributed? Explain

16. QUIZ TIMEE

17. An experiment was conducted by tossing a 50-cent coin on the first trial and then tossing a dice on the second trial. Explain whether this experiment is a binomial experiment or not. An association conducted a survey on the monthly wage earned by most of the working-class Malaysians. The result of the survey showed that 50% of the working-class Malaysians earn less than RM2 000 a month. If 3 workers are randomly selected from a group of workers, explain whether the probability distribution is a binomial distribution or not It is found that a SPM graduate student has three options, namely; continues his studies locally, continues his studies abroad or stops studying. A student is randomly selected from this group of students. Explain whether the outcomes have the characteristics of a binomial distribution.

18. DISCUSSION

19. Calculating probability of an event for binomial distribution

20. p  is the probability of success on any trail. q = 1- p  – the probability of failure n  – the number of trails/experiments r  – the number of successes n C r denotes the number of combinations of  n  elements taken  r  at a time.

21. EXAMPLE 1 Find the probability given p=1/3 , n = 7 and r = 3

22. EXAMPLE 2 Find the probability given q= 2/5 , n = 10 and r = 6

23. EXAMPLE 3 The probability that all the apples in a packet are good is 1/4 . Naimah has bought 9 packets of apples. Find the probability that 3 of the packets contain good apples.

24. EXAMPLE 4 In a survey, 45% of the teenagers owned an iPad. Find the probability that 4 of 6 teenagers own an iPad.

25. TIC -TAC- TOE

26. Exercise Time Refer to worksheet One https://www.youtube.com/watch?v=rPS5gq2G014

27. DISCUSSION

28. Exercise Time Refer to worksheet Two https://www.youtube.com/watch?v=rPS5gq2G014

29. DISCUSSION

30. HOMEWORK SELF – EXERCISE 5.6 PAGE 157 QUESTIONS 1-4

31. Determining the value of mean, variance and standard deviation for a binomial distribution

32. EXAMPLE 1 A study shows that 95% of Malaysians aged 20 and above have a driving license. If 160 people are randomly selected from this age group, estimate the number of Malaysians aged 20 and above who have a driving license. Then, find the variance and the standard deviation of the distribution.

33. EXAMPLE 2 A discrete random variable X has a binomial distribution, which is X ~ B( n , p ) with a mean of 45 and a standard deviation of 3. Find the values of n and p

34. EXAMPLE 3 In a study, it is found that 3 out of 5 men enjoy watching football games. If 1 000 men are randomly selected, find the mean and the standard deviation for the number of men who enjoy watching football games.

35. Exercise Time Refer to worksheet Three

36. DISCUSSION

37. RECALL

38. CONCLUSION