Question 11 5 pts The contingency table below shows the relationship between the gender of survey participants and their political party affiliation from a survey of 802 adults in Minnesota. Define the events: D = The participant is a Democrat F = The participant Is a Female Female Male Republican 105 115 Democrat 150 103 Independent 150 179 Source: Star Tribune Minnesota Poll Based on the last two answers, are the events "being a democrat" and "being a female" independent for this sample? O No, because the probability of being a female is the same as the probability of being a female, given someone is a democrat. O Yes, because the probability of being a female is the same as the probability of being a female given someone is a democrat. O No, because the probability of being a female changes if we know whether they are democrats. O Yes, because the probability of being a democrat is different than the probability of being a democrat given someone is a female.Question 12 5 pts A local hardware store buys 250 snow-shovels in bulk at the beginning of the season to be sold throughout the winter. In a batch of 250 shovels, there will be 15 defective shovels, but the owner does not have time to inspect each one individually so instead she puts them on the floor for sale without inspecting them and offers refunds for anyone who returns a defective shovel. Suppose CBC facility services must buy 10 of the shovels from this store during an unexpected snow storm. What is the probability that at least one of the 10 shovels they purchase is defective? Round your answer to four decimal places as necessary. Question 13 5 pts Among CBC students in the Fall 2019 quarter, 45% of students were enrolled in an English course, 58% of students were enrolled in a Math course, and 21% of students were enrolled in both. If you randomly selected a student in the Fall 2019 quarter, what is the probability that they would be in either an English class or a Math class? Question 14 5 nts Question 14 5 pts The following table is the probability distribution of the random variable X = The number of customers in line at the post ofce during business hours: X P()() 0 0.22 1 0.28 2 0.22 30.15 4 0.08 5 What must be the probability in the missing cell of the table, the probability of seeing 5 people in line? Enter your answer with two decimal places, do not round. Question 15 5 pts The following table is the probability distribution of the random variable X = The number of customers in line at the post ofce during business hours: Calculate the expected (average) number of customers in line. Round to two decimal places as necessary. Question 16 5 pts The following table is the probability distribution of the random variable X = The number of customers in line at the post ofce during business hours: Calculate the standard deviation of the number of customers in line. Round to two decimal places as necessary. Question 17 5 pts Casinos need to know that their games will give the house an advantage, so they set their payouts accordingly. For example, in the game of roulette [as discussed in the quizzes) there are 38 slots, of which 18 are red. The casino bases their payouts on the assumption that the probability of a ball falling in a red slot is 18/38 = 0.4737. Which of the following options best describes 0.4737 in terms of what type of probability it is? 0 Proposed Probability 0 Theoretical Probability O Imprecise Probability 0 Empirical Probability Question 18 Decide if the statement is true or false: Two events are independent if one occurring does not affect the probability of the other occurring. 0 True 0 False Question 19 5 pts A casino offers a game wherein a player can roll one six sided die. If the player rolls a 5, they win. If the player rolls a 1,2, 3, 4, or 6, they lose. If a player bets $5.00 and wins, they will be paid out an additional $20.00. If they lose, they lose their initial $5.00. Find the expected value of the $5.00 bet. Enter your answer rounded to the nearest cent and don't forget, expected values can be negative! Question 20 5 pts Which of the following statements best describes the Law of Large Numbers? 0 The probability of an event cannot be determined without a large number of trials. 0 As the number of trials increases, the empirical (observed) probability of an event will approach the theoretical probability of the event. 0 As the number of trials increases. the theoretical probability of an event will approach the empirical (observed) probability of the event. 0 You should always take as many samples as possible in an experiment. Question 5 5 pts In the game of "Craps", a player rolls two 6-sided dice. Their score on each roll is the sum of the two dice. On the rst roll, a player can: [1} Win automatically by rolling a 7 or 11 [2} Lose automatically by rolling a 2. 3, or 12 [called \"craps"l (3} \"Play on" by rolling any other score besides 2, 3, 7, 11, or 12 What is the probability that a player will win on their rst roll? Round your answer to four decimal places. (Hint: You may want to make a 6x6 square the way I did in the lectures!) Question 7 5 pts At a swim competition, swimmers compete in "heats" (races) against each other for a variety of different events. Suppose a pool has 12 lanes, each one containing a swimmer for a given race. The top three finishers in the race are awarded 1st, 2nd, and 3rd place and recognized for their accomplishment with a trophy. How many different ways can the top three finishers be awarded out of the 12 swimmers? Question 8 5 ptsQuestion 8 5 pts Among CBC students, 18% of students utilize the Academic Success Center (tutoring center). It is also known that 65% of CBC students pass their college-level math course on their first attempt. Of those students that utilize the academic success center, 86% pass their college-level math course on their first attempt. If you randomly select a students at CBC, what is the probability they utilized the tutoring center and passed their college level math class on their first attempt? Round your answer to four decimal places as necessary.D Question 9 5 pts The contingency table below shows the relationship between the gender of survey participants and their political party affiliation from a survey of 802 adults in Minnesota. Define the events: D = The participant is a Democrat F = The participant Is a Female Female Male Republican 105 115 Democrat 150 103 Independent 150 179 Source: Star Tribune Minnesota Poll Calculate P(F). Round your answer to four decimal places as necessary.D Question 10 5 pts The contingency table below shows the relationship between the gender of survey participants and their political party affiliation from a survey of 802 adults in Minnesota. Define the events: D = The participant is a Democrat F = The participant Is a Female Female Male Republican 105 115 Democrat 150 103 Independent 150 179 Source: Star Tribune Minnesota Poll Calculate P(F|D). Round your answer to four decimal places as necessary