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Warm-up 6.2 Binomial Distribution (Day 2) Student of the day! Block 4 Student of the day! Block 5 Review of binompdf and binomcdf 1) It is estimated that 15% of the population suffers some form of mental illness at one point of their lives. In a small company that employs 20 employees. Determine the probability that 2 employees suffer or had suffered some form of mental illness. 2) Delores has a free-throw shooting percentage of 0.65. What is the probability that she makes no more than 5 free throws out of 10 attempts? 6.2 Binomial Distribution Formulas vs. Probability Distribution Formulas Probability Distribution u x xi pi 2 x (x x ) pi 2 i Binomial Distribution u x np 2 x n p (1 p ) 6.2 (Day 2) Binomial Distribution Finding the mean and SD Characteristics of Binomial Distribution: E ( x ) x x n p np 1 p As n increases, the distribution becomes more normal. Shape, Center and Spread H.W. and quiz next block 6.2 E #23-25 Be ready for a quiz on 6.1 and 6.2 You will be given the following formulas on the day of the quiz: 2 2 E(x) x x i p i Var x x ( x i u x ) p i For binomial x nk distributi on np (1 p ) Conclusions from Student Feedback A.P. Statistics Good and should keep Changes and or/ ideas • Printed Notes • More A.P. type questions • Documents on Sharepoint - I have incorporated A.P. • Clearly labeled daily schedule released Qs. • Practice Tests - I will include more A.P. type • Collaborative Work questions in a game or activity • Student of the day! for each chapter. FYI: The calculator can be used on • Reduce # of items on agenda all the exam. There is no non• ½ the class likes activities and calculator section. other don’t. Those of you that want access to - Solution: differentiated A.P. Released Material, bring a instruction, there will be days flashdrive and come in during where you can chose to do an Block 7. I will be happy to give you activity or A.P. type questions files. Multiple Choice Practice on Probability 1) A binomial event has n = 60 trials. The probability of success on each trial is 0.4. Let X be the count of the successes of the event during the 60 trials. What are x and x (s.d) ? (a) 24, 3.79 (b) 24, 14.4 (c) 4.9, 3.79 (d) 4.90, 14.4 (e) 2.4, 3.79 2) Consider repeated trials of a binomial random variable. Suppose the probability of the first success occurring on the second trial is 0.25. What is the probability on the first trial? (a)¼ (b)1 (c)½ (d)1/8 (e)3/16 3) Russell’s parents buy two apples each weekend, and put them in his lunch on two randomly selected weekdays of the following week. What is the probability that Russell gets an apple on exactly one of Monday or Tuesday next week. (a) ( 0 .4 ) 5 2 2 ( 0 .6 ) 3 (b) 2 ( 0 .4 ) ( 0 .6 ) (c) 2 ( 0 .4 )( 0 .6 ) 5 1 5 2 1 4 (d) 4 6 10 (e) 2 2 2 1 5 5 5 4 4) Delores has a free-shooting percentage of 0.65. What is the probability that the first free throw she manages to make is on her 4th attempt. Which of the following would lead to the correct answer? (a) Binomcdf (4, 0.65, 1) (b) Binompdf(4, 0.65, 1) (c) (0.65)(1-0.65)3 (d) 4 ( 0 . 65 )(1 0 . 65 ) 3 1 BONUS QUESTION! At Kennett High School, 5% of athletes play football and some other contact sport, 30% play football, and 40% play other contact sports. If there are 200 athletes, how many play neither football nor any contact sport. Draw a two-way table of the data. Solve for how many students (not percent) play neither football or any contact sport. A.P Statistics Released Question reflecting knowledge of formula Information Given: x 5 and s x 4 y 10 and s y 10 Choices yˆ 8 . 5 0 . 3 x yˆ 5 . 0 3 . 0 x yˆ 5 . 0 2 . 5 x yˆ b 0 b1 x b 0 y b1 x b1 r sy sx yˆ 3 . 0 x yˆ 10 . 0 0 . 4 x Other side to Cumulative Probability worksheet 1. 2. 3. 4. 0.04734 0.38278 0.97175 0.15026 1. 0.114396 2 . 0114396 3. In 20 trials 12 successes is the same as 8 failures. Also if a success is 0.7, then a failure is (1-0.7) = 0.3 . H.W. Etc… 6.2 E #23 – 25 Look at both assignments: A.P. Practice of Ch. 5 and Ch.6 and One-Boy Family Planning Decide which one you want to complete and print it for February 6th (Monday) February 2nd (Thursday) 6.3 Geometric Distribution and Quiz on 6.1 and 6.2 February 6th (Monday) A.P. Statistics finished more details on 6.3 and start on selected assignment 1st day of Ntbk Check February 8th (Wendesday) Practice Ch. 6 Test and finish selected assignment. Ch. 6 Test on Friday February 9th! Answers to Whiteboard Review • • • • • • • 1) a 2) c 3) d 4)c 5) c 6) b 7) c 8) c Bonus! Two-way table should show that 70 athletes are not in either football or a contact sport.