II. Descriptive Statistics (Measures of Position) Direction: Analyze the given problem below. Show your complete solution (if necessary). Answers without solutions will be considered incorrect. Below are the scores of 35 grade 11 students in the final examinations in Mathematics. 61 76 68 82 90 68 93 45 54 54 79 83 58 75 70 63 72 72 77 50 100 72 98 90 96 83 89 86 85 95 88 91 68 65 57 Question - Tasks: 1. What value corresponds to the 40th percentile ? Answer: 2. What is the percentile rank of the score 85? Answer: 3. What value corresponds to ? Answer: 4. If the passing grade is 75, how many percent of the students will fail? Answer: 5. If a grade of at least 90 is required to be included in the honor role, how many percent of the students are qualified? Answer: III. Applications of Normal Distribution Direction: Solve the following problems involving applications of Normal Distributions. Sketch also the graph of the Normal Curve. Show your complete solution. Answers without solution will be consider as incorrect. Strictly no erasures on your final answers. 1. On a test in Statistics, the mean is 65 and the standard deviation is 3. Assuming normality, what is the standard score of a student who receives a score of 60? Answer: 2. Kris gets a score of 85 in a Biology test and 80 in Math test. Scores in the Biology test have a mean of 75 and standard deviation of 5. Score in the Math test have a mean of 76 and standard deviation of 4. In which subject is her standing is better assuming that the scores in the two subjects are normally distributed? Answer: 3. In an English test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, what percent of the score is: a. greater than 65? b. less than 70? c. between 50 and 65? 4. The average weekly income of 1500 workers are Php1500 with a standard deviation of Php80. Assuming that the weekly incomes are normally distributed, find the number of workers who earn: a. between Php1440 and Php1640? b. equal to Php1350? c. greater than Php1400