Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $11. If you roll a 3, 4 or 5, you win $5. Othenvise, you pay $2. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table b. Find the expected profit. SC] (Round to the nearest cent) c. Interpret the expected value. 0 You will win this much if you play a game. 0 If you play many games, on average, you will likely win, or lose if negative, close to this amount. 0 This is the most likely amount of money you will win. d. Based on the expected value, should you play this game? 0 Yes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost. 0 No, this is a gambling game and it is always a bad idea to gamble. 0 Yes, because you can win $11.00 which is greater than the $2.00 that you can lose. 0 No, since the expected value is negative, you would be very likely to come home with less money if you played many games. 0 Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. 61% of all students at a college still need to take another math class. If 4 students are randomly selected, find the probability that a. Exactly 2 of them need to take another math class. c. At least 2 of them need to take another math class. b. At most 2 of them need to take another math class. C] d. Between 2 and 3 (including 2 and 3) of them need to take another math class. [:] Round all answers to 4 decimal places. 81% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 42 owned dogs are randomly selected, find the probability that a. Exactly 36 of them are spayed or neutered. C] b. At most 33 of them are spayed or neutered. c. At least 32 of them are spayed or neutered. C] d. Between 33 and 37 (including 33 and 37) of them are spayed or neutered. C] Round all answers to 4 decimal places. 17% of all Americans live in poverty. If 43 Americans are randomly selected, find the probability that d. Between 6 and 11 (including 6 and 11) of them live in poverty. C] Round each answer to 4 decimal places. About 9% of the population has a particular genetic mutation. 600 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 600. (If possible, round to 1 decimal place.) Assume that a procedure yields a binomial distribution with n = 1156 trials and the probability of success for one trial is p = 81 % . Find the mean for this binomial distribution. (Round answer to one decimal place.) Find the standard deviation for this distribution. (Round answer to two decimal places.) Use the range rule of thumb to find the minimum usual value pZo and the maximum usual value u+20. Enter answer as an interval using square-brackets only with whole numbers. You are playing a card came, and the probability that you will win a game is p = 0.63. If you play the game 731 times, what is the most likely number of wins? (Round answer to one decimal place.) Let X represent the number of games (out of 731) that you win. Find the standard deviation for the probability distribution of X. (Round answer to two decimal places.) The range rule of thumb specifies that the minimum usual value for a random variable is p-Zo and the maximum usual value is |J+26. You already found p, and a for the random variable X. Use the range rule of thumb to find the usual range of X values. Enter answer as an interval using square- brackets and only whole numbers. Assume that the probability of a being born with Genetic Condition B is p = 23/30. A study looks at a random sample of 807 volunteers. Find the most likely number of the 807 volunteers to have Genetic Condition B. (Round answer to one decimal place.) Let X represent the number of volunteers (out of 807) who have Genetic Condition B. Find the standard deviation for the probability distribution of X. (Round answer to two decimal places.) Use the range rule of thumb to find the minimum usual value u-Zo and the maximum usual value p+20. Enter answer as an interval using square-brackets only with whole numbers. When taking a 15 question multiple choice test, where each question has five possible answers, it would be unusual to get C] or more questions correct by guessing alone. Use the Range Rule of Thumb for Unusual Values to answer this question. Give your answer above as a whole number. Suppose that you randomly selected 20 adults. Assume 13% of the population smoke. Round all answers to 2 decimal places. a) Using the Range Rule of Thumb, what is the minimum number of usual smokers we can expect to get out of 20 adults? :1 b) Using the Range Rule of Thumb, what is the maximum number of usual smokers we can expect to get out of 20 adults? :l c) Would it be unusual to randomly select 20 adults and get 19 smokers? 0 Yes, since 19 is not between the maximum and minimum usual values. 0 No, since 19 is between the maximum and minimum usual values