Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Math 245 Lab E sec 7.1-7.6 Recitation time: ___ Name:________________________________ 1. A state lottery draws winning numbers every week. Six different numbers are randomly drawn from the numbers 1 through 50. A player selects six different numbers and pays $1.00 for a ticket. If the player’s six numbers match the six drawn by the state (in any order) then the player receives the jackpot or shares it equally with any other winners. For the following questions you may assume a winner is the sole winner that week. a) How many different combinations of six numbers are possible? b) What is the probability of selecting the winning number? c) If the jackpot is $1 million, find the expected value of a ticket. d) Ray buys a ticket only if the expected value is $1.00 or more. How large must the jackpot be in order for Ray to buy a ticket? 2. If no one wins, the jackpot increases. After a sequence of drawings with no winners, suppose the jackpot increased to $57 million. a) Find the expected value of a ticket with this new jackpot. b) A company decides to buy a ticket for every possible combination of numbers so that they are assured to win the lottery. How many tickets do they need to buy? c) If the company buys all the tickets as described they will win the lottery, but will they make a profit? Explain. 3. Suppose Brian makes 65% of his free throws. a) Find the probability that he makes 3 out of 5 free throws. b) Find the probability that he makes at least 3 out of 5 free throws. 4. It is estimated that a certain brand of automobile tire has a 0.8 probability of lasting 25,000 miles. Out of 4 such tires put on a car, find the probability that at least one will have to be replaced before 25,000 miles. 5. Knowing the measures of central tendency (mean, median, mode) and the measures of dispersion (range, standard deviation) of a data set gives us a more complete view of the nature of the data. The following situations give only a single measure (the mean). Discuss how your view of the situation might change if you also knew the size of the standard deviation. Be creative. Explain the situation with a small standard deviation and then with a large standard deviation. a. The mean monthly rainfall in Waco, Texas is 2.51 inches. * with a small standard deviation * with a large standard deviation b. The average grade on the test last week was 82%. * with a small standard deviation * with a large standard deviation c. “But, officer, I was averaging 50 miles per hour.” * with a small standard deviation * with a large standard deviation 6. Finding the standard deviation of a data set requires a lot of calculations, and the larger the data set is the longer this will take you and the more chances you have to make a mistake in your calculations. For this reason, people dealing with large data sets use calculators or computers to find the standard deviation (as well as other measures). In this problem you get a chance to practice using the statistics capabilities of your calculator. The table below gives the population of each Oregon county, as determined by the 2000 census. County Baker Benton Clackamas Clatsop Columbia Coos Crook Curry Deschutes Douglas Gilliam Grant Harney Hood River Jackson Jefferson Josephine Klamath Lake Lane Lincoln Linn Malheur Marion Morrow Multnomah Polk Sherman Tillamook Umatilla Union Wallowa Wasco Washington Wheeler Yamhill Population 16,741 78,153 338,391 35,630 43,560 62,788 19,184 21,137 115,367 100,399 1,915 7,935 7,609 20,411 181,273 19,009 75,726 63,775 7,422 322,977 44,479 103,069 31,615 284,838 10,995 660,486 62,380 1,934 24,262 70,548 24,530 7,226 23,791 445,342 1,547 84,992 a. What was the mean population of an Oregon county in 2000? b. Explain what your answer to part a tells you. c. What was the standard deviation of the county populations in 2000? d. Explain what your answer to part c tells you. e. How many counties had populations close to the mean? (You will have to decide what is “close”, and explain your decision.)