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##### STATS Assignment Problems-Two fair dice are rolled and the number of dots

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Question;INSTRUCTIONS? Make sure your answers are as complete as possible and show your work/argument step-by-step. In particular, when there are calculations involved, you should show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from program software packages will not be accepted.1. Two fair dice are rolled and the number of dots facing up is added. Fill in the column for the probabilities.X= sum of the dots facing up P(X)2 3 4 5 6 7 8 9 10 11 12Consider the following probability table to answer the questions 2 and 3.x P(x)4 0.018 0.0312 0.0520 0.0924 0.5025 0.2826 0.042. Find the mean or expected value of this probability distribution.3. Find the standard deviation of this probability distribution.4. A sample of 4 people is selected from a group of six people named Ali, Bina, Chris, David, Erin and Frank. a) How many such samples are possible?b) What is the probability a sample containing Bina and Chris is selected.Consider the following for the questions #5,#6,#7A fair die is rolled three times and the number of dots facing up is noted.5. How many elements does the sample space have?6. What is the probability that the three rolls will have different numbers?7. What is the probability that all the three rolls will have even numbers?8. How many different simple random samples of size 8 can be selected from a population consisting of 70 people? (you may use the combinations)9. A lottery game named Mega millions let a player choose a set of 5 numbers from a set of numbers 1 to 56 and another set of 1 number from 1 to 46. How many different selections can be made? (you may use the combinations)10. A strabismus surgery has a probability of 0.9 of success in the first attempt and a probability of 0.98 of success in the second attempt. Use the techniques of tree diagrams to find the probability the probability that the surgery will be successful within two attempts. (round four digits after the decimal)11. A computer manufacturer uses graphic cards made by two companies N and I. They are using the cards made by N in 80% of the computers and made by I on 20% of the computers. They have found that 2% of the cards made by N have been defective and 5% of the cards made by I have been defective. A computer owner has reported a problem with the graphic card. Use the techniques of tree diagrams to find the probability that the card is made by I. (round four digits after the decimal)Consider the following context for the questions #15,#16,#17,#18In a certain region, 91% of the people can speak English, 44% can speak Spanish, and 40% can Speakboth English and Spanish. One person is randomly selected from this region. Use Venn Diagrams to15. Find the probability that the selected person can speak only one of the language from out of English and Spanish.16. Find the probability that the selected person can speak neither of the two languages (English or Spanish.)17. Find the probability that the selected the person can speak English but not Spanish.18. Find the probability that the selected person can speak English, given that the person can speak Spanish.For the questions #19,#20, consider a deck of 52 cards as shown below#19. The deck is well shuffled, card is drawn and a card is drawn, find the probability that the card is a face card, i.e. a Jack or Queen, a King or an ace.#20. A game charges $1.00 to play and pays $4.00 if a card drawn from a well shuffled deck such as above is a face card, other wise the the player loses the money. Find the expected expected value of the gain for this player.You may fill the following table to answer this questionOutcome Gain ProbabilityFace Card $4-$1=$3 No Face Card $0-$1=?$1 21. 22.23.24.b. Find the probability of 3 or fewer Mexican-Americans among 12 jurors.c. Which probability is relevant for determining whether 3 jurors among 12 is usually low: the result from part (a) or part (b)?d. Does 3 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? Why or why not?25.26.27.b. Beginning with WWC, make a complete list of the different possible arrangemnts of two correct answers and one wrong answer, then find the probability for each entry in the list. c. Based on the preceding results, what is the probability of getting exactly two correct answer when three guesses are made?28.29.30.31.32.b. Assuming that the 50% rate in part (a) is correct, find the range of usual values for the numbers of graduates among 380 who stay at their first job less than two years.c. Find the actual number of surveyed graduates who stayed at their first job less than two years. Use the range of values form part (b) to determine whether that number is unusual. Does the result suggest that the headline is not justified? d. The statement, ?Alumni who opted-in to receive communications form the website were invited to participate in the online poll, and 380 of them completed the survey,? was given as part of the description of the survey methods used. What does that statement suggest about the results?33.USE THE TABLES BELOW TO ANSWER QUESTION 34 TO 44

Paper#61650 | Written in 18-Jul-2015

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