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I need help with my attached statistics homework. THIS IS NOT A Quiz. I also screenshot some of the questions multiple times to show the

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I need help with my attached statistics homework. THIS IS NOT A Quiz. I also screenshot some of the questions multiple times to show the select options. This is all the relevant information.

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Professor Duque will participate in a lottery that will be played by five hundred participants. He buys a ticket for five dollars. If the lucky randomly selected winner gets one hundred dollars as a prize, what would Duque's expected winnings or losses be? (Show your calculations, interpret your results, and make sure you answer the question!) (17 points)An experiment is rolling a fair die and then flipping a coin. a} State the sample space. List outcomes separated by commas. Use notation like 1H to mean you rolled a 1 on the die and flipped heads on the coin. {I I} b] Find the probability of getting a tail. Leave your answer as a fraction. :1} Find the probability of getting a a. Leave your answer as a fraction. d] Find the probability of getting a 3 or a head. Leave your answer as a fraction. e} Find the probability of getting a 1 and a tail. Leave your answer as a fraction. An experiment is to draw '1 card from a fair deck of playing cards. a} If you were to list the sample space. how many equally likely outoomes would it haye? b] Find the probability of getting a a. Lease your answer as a fraction. I I :1} Find the probability of not getting a heart. Leave your answer as a fraction. I I d] Find the probability of getting a club. Leave your answer as a fraction. I I e} Find the probability of getting a s or a spade. Leave your answer as a fraction. I I In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. a) Find the probability of winning if you pick the number 3 and it comes up on the wheel. Leave your answer as a fraction. b) Find the probability of an odd number coming up on the wheel. Leave your answer as a fraction.Suppose the spinner shown below is used for a game. 12 11 2 10 3 A 5 7 6 Find the probability of each event below. Write all probabilities as fractions in simplest form. (a) P(spin 6) = (b) P(spin 7 or 12) = (c) P(spin a multiple of 4) = (d) P(spin a number more than 7) =Consider two events, A and B, with the following probabilities: P(A) = 0.42 P(B) = 0.36 P(An B) = 0.12 Find the probability of A U B . Round to the nearest hundredth as needed. Hint: You can use a Venn diagram or the Additive Rule for probability. P(A U B) =Here is the probability model for the blood type of a randomly chosen person in the United States. Brood Tree nun \"mm Maria has type B blood. She can safely receiye blood transfusions from people 1with blood types 0 and B. What is the probability that a randomly chosen American can donate blood to Maria? Give the answer as a decimal. A jar contains 10 red marbles numbered 1 to 10 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability of the given event, please show your answers as reduced fractions. (a) The marble is red. P(red)= (b) The marble is odd-numbered. P(odd)= (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =Let A and B be mutually exclusive events, such that P(A) = 0.7295 and P(B) = 0.1734 . Find the following probabilities: P(A and B)= (Round the answer to 4 decimals) P(A or B)= (Round the answer to 4 decimals)On a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong? Give your answer as a fractionGiving a test to a group of students, the grades and gender are summarized below A B C Total Male 12 10 11 33 Female 9 4 7 20 Total 21 14 18 53 If one student is chosen at random, Find the probability that the student did NOT get an "C"A bag of MOM's has 5 red, 6 green, 2 blue, and 4 yellow M&M's. Suppose you randomly select two MOM's from the bag one at a time without replacing the first MOM. Let A = first MOM is yellow and B = second MOM is red. Find the following probabilities. (Write your answers as fractions.) a) P(A) b) P(B | A) = c) P(A and B) =A bag of MOM's has 4 red, 2 green, 6 blue, and 3 yellow M&M's. Suppose you randomly select two MOM's from the bag one at a time with replacing the first M&M. Let A = first MGM is red and B = second MOM is blue. Find the following probabilities. (Write your answers as fractions.) a) P(A) = b) P(B | A) = c) P(A and B) =A test was given to a group of students. The grades and gender are summarized below A B C Total Male 9 10 4 23 Female 3 8 17 28 Total 12 18 21 51 If one student is chosen at random from those who took the test, Find the probability that the student was female GIVEN they got a 'C'.A test was given to a group of students. The grades and gender are summarized below A B C Total Male 18 5 14 37 Female 11 3 7 21 Total 29 8 21 58 If one student is chosen at random from those who took the test, Find the probability that the student got a 'B' GIVEN they are male.Suppose a math class contains 31 students, 19 females (three of whom speak French) and 12 males (four of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.Find the mean of this probability distribution. Round your answer to one decimal place. H : Find the standard deviation of this probability.r distribution. Give your answer to 1 decimal places. gr: The probability distribution for the number of students in Statistics classes offered at a small college is given, but one value is missing. Fill in the missing value, then answer the questions that follow. 'r'ou may round your answers to two decimal places, if necessary. Find the mean number of students in a Statistics class at the college: Find the standard deviation of the number of students in a Statistics class at the college: Find the mean and standard deviation of a probability distribution. As a special case of the mean, be able to compute the expectation in a game, given the profit associated with each possible outcome. Find the missing probability, P(-1), and then find the mean and standard deviation for this probability distribution. You may round your answers to two decimal places. C P(x) -5 0.12 -1 0.07 2 0.16 4 0.08 Mean = Standard Deviation =A company estimates that 0.596 of their products will fail after the original warranty period but within 1 years of the purchase. with a replacement cost of SEEK}. If they offer a 2 year extended warranty for 531, what is the company's expected 1value of each warranty said? A bag contains 1 gold marbles, 8 silver marbles, and 30 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?Apoll is given, showing 35% are in favor of a new building project. If 113 people are chosen at random answer the following. a} Which is the correct wording for the random variable? b] Pick the correct symbol: = 113 c} Pick the correct symbol: = I135 d] What is the probability that exactly 39 of them are in favor of a new building project? Round final answer to 4 decimal places. I I e} What is the probability that less than 39 of them are in favor of a new building project? Round final answer to 4 decimal places. I I f} What is the probability that more than 39 of them are in favor of a new building project? Round final answer to 4 decimal places. I I g} What is the probability that exactly 41 of them are in favor of a new building project? Round final answer to 4 decimal places. I I h} What is the probability that at least 41 of them are in favor of a new building project? Round final answer to 4 decimal places. I I i] What is the probability that at most 41 of them are in favor of a new building project Round final answer to 4 decimal places. I I A poll is given, showing 35% are in favor ofa new building project. If 113 people are chosen at random, answer the following. a] Which is the correct wording for the random variable? 1" Eelect an answer rv K = is in favor of a new building project i: rv X = a randomly selected person that is in favor of a new building project rv K = all people that are in favor of a new building project c: rv K = the probability that a randomly selected person is in favor of a new building project rv X = the number of 123 randomly selected people that are in favor of a new building project d rv K = a randomly selected person rv X: the number of randomly selected people that are in favor of a new building project Round final answer to 4 decimal places. | l e} What is the probability that less than 39 of them are in favor of a new building project? Round final answer to 4 decimal places. | I f} What is the probability that more than 39 of them are in favor of a new building project? Round final answer to 4 decimal places. | I g} What is the probability that exactly 42 of them are in favor of a new building project? Round final answer to 4 decimal places. | l h} What is the probability that at least 41 of them are in favor of a new building project? Round final answer to 4 decimal places. | l i} What is the probability that at most 42 of them are in favor of a new building project Round final answer to 4 decimal places. | l A poll is given, showing 35% are in favor of a new building project. If 113 people are chosen at random, answer the following. a} Which is the correct wording for the random variable? Select an answer V b] Pick the correct symbol 1" ? = 123 c} Pick the correct symbol I I135 d] What is the probability Ictly 39 of them are in fayor of a new building project? Round final answer to 4 l places. | | FXIXJUQZW e} What is the probability s than 39 of them are in favor of a new building project? Round final answer to 4 decimal places. | | f} What is the probability that more than 39 of them are in favor of a new building project? Round final answer to 4 decimal places. | | g} What is the probability that exactly 4?. of them are in favor of a new building project? Round final answer to 4 decimal places. | | h} What is the probability that at least 42 of them are in favor of a new building project? Round final answer to 4 decimal places. | | i] What is the probability that at most 42 of them are in favor of a new building project Round final answer to 4 decimal places. | | a poll is given, showing 35% are in favor of a new building project. If 113 people are chosen at randon answer the following. a] Which is the correct wording for the random variable? b] Pick the correct symbol: = 113 c} Pick the correct symbol v" ? -IJ.35 d] What is the probability ictly 39 of them are in favor of a new building project? Round final answer to 4 l places. I I e} What is the probability s than 39 of them are in favor of a new building project? omlextz ['1] Round final answer to 4 -.. .....;l places. I I f} What is the probability that more than 39 of them are in favor of a new building project? Round final answer to 4 decimal places. I I g} What is the probability that exactly 42 of them are in favor of a new building project? Round final answer to 4 decimal places. I I b} What is the probability that at least 42 of them are in favor of a new building project? Round final answer to 4 decimal places. I I i] What is the probability that at most 41 of them are in favor of a new building project Round final answer to 4 decimal places. I I Assume this year's flu vaccine has a 60% chance of being effective. If the vaccine is given to 332 randomly selected people, answer the following. a} l|."'."hich is the correct wording for the random variable? b] Pick the correct symbol: = 332 c} Pick the correct symbol: = 0.6 d] What is the probability that exactly 203 of them did not get the flu? Round final answer to 4 decimal places. I I e} What is the probability that less than 203 of them did not get the flu? Round final answer to 4 decimal places. I I f} What is the probability that more than 203 of them did not get the flu? Round final answer to 4 decimal places. I I g} What is the probability that exactly 204 of them did not get the flu? Round final answer to 4 decimal places. I I h} What is the probability that at least 204 of them did not get the flu? Round final answer to 4 decimal places. I I i] What is the probability that at most 204 of them did not get the flu Round final answer to 4 decimal places. I I Assume this year's flu vaccine has a sos chance of being effective. If the vaccine is given to 332 randomly selected people, answer the following. a] Which is the correct wording for the random variable? 1" Select an answer rv X: the number of randomly selected people who got the vaccine that did not get the flu in rv X = the number of 332 randomly selected people who got the vaccine that did not get the flu rv X = the probability that a randomly selected person who got the vaccine did not get the flu c rv X = did not get the flu rv X = all people who got the vaccine that did not get the flu d rv X = a randomly selected person who got the vaccine that did not get the flu rv X = a randomly selected person who got the vaccine Round final answer to 4 decimal places. I I e} What is the probability that less than 203 of them did not get the flu? Round final answer to 4 decimal places. I I f} What is the probability that more than 203 of them did not get the flu? Round final answer to 4 decimal places. I I g} What is the probability that exactly 254 of them did not get the flu? Round final answer to 4 decimal places. I I h} What is the probability that at least 264 of them did not get the flu? Round final answer to 4 decimal places. I I i} What is the probability that at most 204 of them did not get the flu Round final answer to 4 decimal places. I I Assume this year's flu vaccine has a 50% chance of being effective. If the vaccine is given to 332 randomly selected people, answer the following. a} Which is the correct wording for the random variable? Select an answer V b] Pick the correct symbol 1" ? = 332 c} Pick the correct symbol 3 =|J.6 d] What is the probability I; Ictly 203 of them did not get the flu? X Round final answer to 4 X l places. I I p e} What is the probability N 3 than 203 of them did not get the flu? Round final answer to 4 decimal places. I I f} What is the probability that more than 203 of them did not get the flu? Round final answer to 4 decimal places. I I g} What is the probability that exactly 204 of them did not get the flu? Round final answer to 4 decimal places. I I h} What is the probability that at least 264 of them did not get the flu? Round final answer to 4 decimal places. I I i] What is the probability that at most 204 of them did not get the flu Round final answer to 4 decimal places. I I Assume this year's flu vaccine has a 60% chance of being effective. If the vaccine is given to 332 randomly selected people, answer the following. a] l|."v'hich is the correct wording for the random variable? Select an answer in? b] Pick the correct symbol: = 332 c} Pick the correct symbol 4" 2 -0.6 d] What is the probability :ctlyr 203 of them did not get the flu? Round final answer to 4 l places. | | e} IWhat is the probability s than 203 of them did not get the flu? WIZQXXIU3 Round final answer to 4 \"c"..ol places. | | f} What is the probability that more than 203 of them did not get the flu? Round final answer to 4 decimal places. | | g} What is the probability that exactlyr 204 of them did not get the flu? Round final answer to 4 decimal places. I I h} What is the probability that at least 204 of them did not get the flu? Round final answer to 4 decimal places. | | i] What is the probability that at most 204 of them did not get the flu Round final answer to 4 decimal places. | | In the United States, 40% of the population has type A blood. Suppose 45 people from the U.5. are randomly chosen. Use the formula for binomial probabilities Pa) = (3m :0)\" t to find the probability that exactly 3 of the f: people sampled haye type A blood. {a} First fill in the details of the binomial probability formula: 13(3) = { i { i [b] The probability, accurate to 4 decimal places, is Assume that a procedure yields a binomial distribution with n = 34 trials and the probability of success for one trial is p = 0.17. 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.) Will the probability histogram for the binomial random variable be approximately bell shaped? O No, this is not bell shaped since np(1 - p) 10 O Yes, this is bell shaped since np(1 - p) > 10

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