1 Suppose flights at a large metropolitan airport are on-time 68% of the time and late 32% of the time. We want to use a table of random digits to simulate flight status (on-time or late), so we'll assign 01, 02, ... , 68 to represent on-time flights, and 69, 70, ... , 99, 00 to represent late flights. You want to estimate the probability that 15 or more flights out of 20 will be on-time at this airport. You simulate 20 flights 25 times and get the following numbers of on-time flights: 11 15 14 8 17 14 16 15 17 17 15 9 13 16 12 18 14 16 13 15 16 14 18 14 9 What is your estimate of the probability? 0.16 0.48 0.52 0.56 13 2 Computer voice recognition software is getting better. Some companies claim that their software correctly recognizes 98% of all words spoken by a trained user. To simulate recognizing a single word when the probability of being correct is 0.98, you could use random digits as follows: Two digits simulate one word; 00 to 97 mean \"correct.\" Two digits simulate one word; 00 to 98 mean \"correct.\" One digit simulates one word; 0 to 9 mean \"correct.\" Three digits simulate one word; 001 to 098 mean \"correct.\" 3 You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. To simulate an outcome with probability 0.11 you could look at two digits in the random number table; the outcome occurs if the digits are 11. look at two digits in the random number table; the outcome occurs if the digits are any of 00, 01, ... , 11. look at two digits in the random number table; the outcome occurs if the digits are any of 00, 01, ... , 10. look at two digits in the random number table; the outcome occurs if the digits are any of 01, 02, ... , 11. Both (C) and (D) are correct simulations. 4 A friend rolls a cheap 6-sided die many times. He reports that the probabilities of the possible outcomes are about as follows: Outcome 1 2 3 4 5 6 Probability 0.2 0.2 0.2 0.1 0.1 0.2 Using the probabilities above, what is the expected outcome when rolling this die? 3 3.3 3.5 4 4.5 5 Suppose you know the percentage of foul shots a basketball player makes during the season. You want to estimate the expected number of shots made in 10 shots. You simulate 10 shots 25 times and get the following numbers of shots made: 7976375656756685639677879 Your estimate is: 5.5 6 6.4 6.7 7 6 Choose an American household at random and ask how many computers that household owns. Here are the probabilities as of 2009: Number of computers 0 1 2 3 4 5 Probability 0.241 0.412 0.214 0.083 0.032 0.018 What is the expected number of computers owned by a randomly chosen household? 1.412 1.307 2.214 2 2.5 7 A game involving a pair of dice pays you $4 with probability 16/36, costs you $2 with probability 14/36, and costs you $6 with probability 6/36. If you play this game many times, in the long run how will your actual average gain per play compare with your answer to the previous question? smaller bigger about the same the question can't be answered