MATH 1F92 - Assignment # 4 Due: Friday, Noverm 13, 2015 by 11:00 AM Assignments must have a cover page (refer to the course outline). Please write on one side of the page only and show ALL your work. Answer questions with sentences. Include any printout for a question with the question and clearly label the printout with the question number and part. You can leave the probability in fraction format or decimal format (keep 4 decimal places). Read Sections 5.5, 6.1, 6.2, and 6.3 Question 1 A social security number consists of nine digits in a particular order, and repetition of digits is allowed. If randomly selecting digits for one social security number, what is the probability that you select the social security number of the President of United State (Please leave result as a fraction)? Question 2 How many different ways can you touch two or more fingers to each other on one hand? Question 3 Winning a jackpot requires that you select the correct numbers between 1 to 59 and, in a separate drawing, you must also select the correct single number between 1 and 39. Find the probability of winning the jackpot (Please leave the result as a fraction). Question 4 The table below describes results of roadworthiness tests of Ford Focus cars that are 3 years old (based on data from the department of Transportation). The random variable x represents the number of cars that failed among six that were tested for roadworthiness. Page 1 of 3 x 0 1 P(x) 0.377 0.39 9 2 3 4 0.17 6 0.041 0.00 5 5 6 0.00 1 0.001 a. Verify that this is a discrete probability distribution. b. Compute and interpret the mean of the random variable x. c. Find the standard deviation of the random variable x. d. Find the probability of getting three or more cars that fail among six cars tested. Question 5 Based on past history, an airline determines that an average of 5% of people with reservations don't show up for their flights. Consequently, the airline routinely overbooks flights, accepting 310 reservations for a plane that seats 300 passengers. This system can be modelled by a binomial distribution with n= 310, and p = the probability that someone with a reservation does show up. a) What probability would you need to find to determine that, when 310 reservations are accepted for a particular flight, there are more passengers than seats? Use Excel Binom.dist(x, n, p, 1) to find this probability. b) Based on your answer to a), is there need for concern, i.e. should the airline's policy on overbooking be changed? Explain. Question 6 In the 1990s, possible abuse of minorities by Philadelphia police officers was investigated. One study analyzed whether African-American drivers were more likely than others to be targeted for traffic stops. They studied the results of 262 independent police car stops during one week in 1997 and found that 207 of the drivers stopped were African-American. At that time, 42.2% of Philadelphia's population was African-American. a) Find the mean and standard deviation for the random variable X, the number of African-Americans stopped in 262 traffic stops. b) Interpret the mean. Page 2 of 3 c) Is there evidence to suggest that there was racial profiling in Philadelphia at that time? Explain. Page 3 of 3