Ryan Smith MAT-131-DE03A 9/21/16 Lab 2 Stroke Rates in Relation to Life Expectancy Around The Globe PART 1: V1 Qualitative Data (Continents) A. B. C. D. This data doesn't really tell much but the frequency of countries randomly selected by the generator I used through Randomlists.com. It is definitely easier to compare these numbers using the Pareto graph, especially with the Americas and Africa's numbers so close to each other. Looking at the pie chart you may think they have the same value. PART 2: V2 Quantitative Data (Stroke Rates per 10,000) A. # of Stroke Rates Frequency (f) 22-47 48-73 74-99 100-125 126-151 152-175 14 7 4 4 6 5 B. It seems this histogram is skewed right. Relative Frequency (rf) 0.35 0.175 0.1 0.1 0.15 0.125 Class Mid-Point 34.5 60.5 86.5 112.5 138.5 163.5 PART 3: V3 Quantitative Data (Life Expectancy) A. Life Expectancy 50-56 57-63 64-70 71-77 78-84 B. Frequency (f) 4 2 4 14 16 Relative Frequency (rf) 0.1 0.05 0.1 0.35 0.4 Class Midpoint 53 60 67 74 81 C. D. Looking at the data you can see that the rate of death increases dramatically in the 70+ region. I would personally prefer to use the polygon graph as I think it more effectively illustrates the life span of person and where most people unfortunately pass. MATH 131 Lab 4 8/16 The goal of this lab is to define a binomial experiment and find binomial probabilities by two different methods. (2 points) Part 1: Experiment Definition A. Return to Lab 2, V1. Define \"success\" for your qualitative data to be the category with the largest relative frequency from your Lab 2 Part 1A table. ______________________ B. Name what a failure will be for your qualitative data. ____________________________ (If you have more than one category, combine and name them as \"Others\") C. What is your value for p, the probability of success from A? _______________________ D. What is your value for q? _______________________ You will not actually be collecting any new data for Parts 2 and 3. You will be finding probabilities associated with specific numbers of trials of the experiment stated. (4 points) Part 2: Binomial Formula (n=3) A. Using the correct formula and showing your calculations, create a table as noted here for three independent trials. ( is the number of successes in 3 trials.) 0 x 3 . x Calculations: x 0 P( x) 1 2 3 B. What are the two criteria for a valid probability distribution? Use them to verify that your probability distribution from part A is valid. Check the sum of your own probabilities. (1) (2) C. Find the mean of the probability distribution from part A using two different methods (one from Section 4.1 and one from Section 4.2). Show your work. (1) (2) 1 MATH 131 Lab 4 (4 points) 8/16 Part 3: Binomial Table or Computer (n=10) A. Using the binomial table in your text or the computer (See computer notes below), create a table similar to Part 2 but for n = 10 trials. x is number of successes. x P( x) 0 1 2 3 4 5 6 7 8 9 10 B. Using the table above to answer the following. For parts 2-4, show the individual values that you are adding up, as well as the total. The answer alone is not sufficient (1) What is the probability of exactly 10 successes? (2) What is the probability of no more than 3 successes? (3) What is the probability of at least 7 successes? (4) What is the probability of between 2 and 9 successes (inclusive)? StatCrunch Stat Calculators Binomial Enter n = 10 and the value for p from Part 1. Select x = 0 and hit Compute. Continue for all values of x in your chart. Minitab Type the x values (0 - 10) in C1. Select Calc Probability Distribution Binomial Choose Probability Enter Number of Trials and the Probability of Success for your data Tell Minitab that the x values are in C1 and that you want the probabilities stored in C2 by entering C1 as the Input Column and C2 for Optional Storage 2 NAME 1. Iraq 2. Armenia 3. Turkey 4. Hait 5. Morocco 6. Austria 7. Netherlands 8. Syria 9. Egypt 10. Chad 11. Jamaica 12. Venezuela 13. Mexico 14. Norway 15. Lebanon 16. Iceland 17. Thailand 18. Barbados 19. Guinea 20. Mongolia 21. Yemen 22. Estonia 23. Chile 24. Germany 25. Botswana 26. United States 27. Uganda 28. Vietnam 29. Dominica 30. Denmark 31. Benin 32. Malta 33. Saint Lucia 34. Spain 35. Nigeria 36. Saudi Arabia 37. Croata 38. Switzerland 39. United Kingdom 40. Georgia V1 - Continent Asia Asia Asia Americas Africa Europe Europe Asia Africa Africa Americas Americas Americas Europe Europe Europe Asia Americas Africa Asia Asia Europe Americas Europe Africa Americas Africa Asia Americas Europe Africa Europe Americas Europe Africa Asia Europe Europe Europe Asia V2 - Stroke Rates per 10,000 81 133 117 150 62 26 22 112 110 163 63 54 39 33 53 29 23 41 166 151 84 58 45 31 112 163 151 173 87 39 148 44 68 29 149 50 89 22 37 169 V3 - Life Expectancy 71 74 73 71 74 73 63 77 80 81 69 73 49 73 74 75 82 77 81 74 75 60 69 65 74 78 88 54 80 59 73 77 79 61 80 77 81 82 80 76