1 The Police Headquarters classifies crimes by age (in years) of the criminal and whether the crime is violent or non-violent. As shown below, a total of 150 crimes were reported last year. Age (in years) Type of Crime Under 20 20 to 40 Over 40 Violent 32 43 12 Non-violent 13 34 16 Suppose that a case is selected at random. Answer the following questions. Round up all answers to 3 decimal places (3 d.p.) a) What is the probability of selecting a case to analyze and finding it involved a violent crime? [1 mark] b) What is the probability of selecting a case to analyze and finding the crime was committed by someone 40 years old and below? [1 mark] c) What is the probability of selecting a case involved a violent crime or an offender less than 20 years old? [3 marks] d) Given that a violent crime is selected for analysis, what is the probability the crime was committed by a person under 20 years old? [3 marks] e) Are 'violent' and 'under 20 of age' mutually exclusive events? Explain. [2 marks] Question 2 Medical billing errors and fraud are on the rise. According to the Medical Billing Advocates of Copacabana, 80% chances that the medical bills that you get are not right. Suppose that the medical billing errors follow a binomial distribution. A sample of 10 medical bills is selected. a) What is the probability that exactly 4 medical bills will contain errors? [3 marks] b) What is the probability that at least two will contain errors? [3 marks] c) What is the expected number of medical bills that contain errors? [2 marks] Question 3 A crossword puzzle is published in The Enquirer each day of the week, except Sunday. A man is able to complete on average 7 out of 10 of the crossword puzzles. a) Find the expected value and standard deviation of the number of completed crossword puzzles in a given week. [2 marks] b) What is the probability that he will complete at least 4 in a given week? [5 marks] c) Given that he completes the puzzle on Monday, find the probability that he will complete at least 3 crossword puzzles in the rest of the week. [3 marks] Question 4 A set of final exam grades in QBA241 last Spring semester was found to be normally distributed with a mean of 75 and a standard deviation of 8. a) What is the probability of getting a grade less than 85 on this exam? [3 marks] b) Only 1% of the students taking the test scored higher than what grade? [3 marks] c) If the professor grades on a curve (gives A's to the top 5% of the class regardless of the score), are you better off with a grade of 85 on this exam or a grade of 69 on a different exam where the mean is 63 and the standard deviation is 3? [6 marks] Assignment 2, Fall 2016/2017 Page 1