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2 9. Statistical distributions.

2 9. Statistical distributions. a. SERRA. 29A&B. Discrete random variables and discrete probability distributions. Reminder : Title > Theory >Examples (if necessary) > Exercises> Correct ( ✓ , ✗ ,?) 20% hwk > Extra (even + PS + HL) New: Daily Miniquiz . Class work:

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2 9. Statistical distributions.

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  1. 29. Statistical distributions. a. SERRA

  2. 29A&B. Discrete random variables and discrete probability distributions. • Reminder : Title > Theory >Examples (if necessary) > Exercises> Correct (✓, ✗,?) 20% hwk> Extra (even + PS + HL) • New: Daily Miniquiz. • Class work: • Continuous vs Discrete: Measuring vs counting. • Discrete random variables and probability distribution associated with it. • EG. Exercise 29B:4 Page 713 • Individual work: • Examples 1,2,3 and 4: Do them & check your answers. • Exercise 29A: 1,3 • Exercise 29B: 3, 7 • Extra: even numbers 29 A and B.

  3. 29C. Expectation. • Class work: • Eg. I am a very good goal keeper . The probability of a penalty kick scoring a goal if I am goalie is only 0.7. How many goals can we EXPECT if 10 LAS students have the chance to try my skills? • Individual work: • Example 5: Do it & check your answers. • Exercise 29C: 1,7, 11, 13 • Extra: Even numbers

  4. 29D. The mean and standard deviation of a discrete random variable. • Class work: • Link from mean (Unit 18) and exercises 29C: 11, 13. • Formulae in blue box in page 719. • Eg. 6 page 721. • Individual work: • Examples 6 and 7: Do them & check your answers. • Exercise 29D: 3,5,7 • Extra: Even numbers

  5. 29 E. The binomial distribution. • Class work: • Sampling with and without replacement: Binomial and the hypergeometric distributions. • Binomial experiment (independent trials with two possible outcomes (yes/no, success/failure, etc.) • Example: • exercise 6 page 724. 2ndVARS (Distr)> Binompdf (20,0.5,10)=0.176 (!) • 2ndVARS (Distr)> Binomcdf(20,0.5,10)=0.588 (!) • Individual work: • Example 8: Do it & check your answers. • Exercise 29 E: 3, 7, 9 • Even numbers.

  6. 29F. Mean and standard deviation of a binomial random variable. • Class work: • Review previous. Formulae page 724. NB Proof not needed. • Example: Exercise 6 in page 727. • Individual work: • Examples 9 and 10: Do them & check your answers. • Exercise 29F: 1 and 5. • Extra: Even numbers

  7. 29G. Normal distributions. • Class work: • Discrete random variables > continuous random variables. • Probability density function. Real life examples (some on page 728). • Geometrical properties and significance of the mean and standard deviation in a bell-shaped curve. (bottom page 729 and 730). • Example: Exercise 6 in page 732. See online videos: • GDC>DISTR>DRAW>ShadeNorm(min,max,mean,sd). • GDC>DISTR>Normalcdf (min,max,mean,sd). • Individual work: • Example 11: Do it & check your answers. • Exercise 29G1: 3 and 7. • Exercise 29G2: 1 • Extra: Even numbers

  8. 29H. The standard normal distribution. • Class work: • The need to have a very special example. Z-distribution. • Models and tables. Page 735. • Example Exercise 29H2.2 Page 738 using table and GDC>DISTR>normalcdf (min,max) • Individual work: • Examples 12, 13 and 14: Do them & check your answers • Exercise 29H1:3 • Exercise 29H2:3 (note that sigma=0.93mm and not 0.93m) • Exercise 29H3:1 • Extra: Even numbers

  9. 29I. Applications of the normal distribution. • Class work: • Example 8 page 741 (see online video). . • Example 2 page 740 Three ways to solve it: • GDC>DISTR>DRAW>ShadeNorm(min,max,mean,sd) • GDC>DISTR>Normalcdf (min,max,mean,sd). • GDC>DISTR>Normalcdf (minZ,maxZ). • Individual work: • Examples 15 and 16: Do them & check your answers. • Exercise 29I: 1,3,5 • Extra: Even numbers

  10. Problem solved step by step (video online) • A student scored 70 for a Science exam and a 66 for Geography. The class scores are normally distributed with a mean and a standard deviation for Science of 60 and 10 and Geography for 50 and 12. • In which subject did the student achieve a higher standard? • What percentage of others achieved lower marks in each subject? • c ) What was the maximum score obtained by the 80% weakest Science students? • What was the minimum score obtained by the top 20% Geography students? • Answer: • a- Science: Z= (70-60)/10 = 1 < Geography Z= (66-50)/12 = 4/3 (aprox. 1.33) • b - Normalcdf (-1000,1)= 0.841 < Normalcdf (-1000,66, 50,12)= 0.909 • c- (X-60)/10 = invNorm (0.8)= 0.842 therefore x=68.4 • d- (X-50)/12 = invNorm (0.8)= 0.842 therefore x=60.1

  11. Review unit 29 • INDIVIDUAL WORKHOMEWORK • Review Set 29A. (Do, correct your answers and write down score (total and percentage “%”) • Mock test: Same • Extra: Create an online quiz using Google forms and share it with the group. Please make sure your answers are correct. A positive in homework and/or in professionalism can be awarded if you do this task! • Next> Test

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