4 Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete parts (a) through (e). 7 8 0. 0.07 1 5 a) Use the probability distribution to find the mean of the probability distribution. U= (Round to the nearest tenth as needed.) (b) Use the probability distribution to find the variance of the probability distribution. sigma squared equals (Round to the nearest tenth as needed.) (c) Use the probability distribution to find the standard deviation of the probability distribution. (Round to the nearest tenth as needed.) (d) Use the probability distribution to find the expected value of the probability distribution. 8\\ (Round to the nearest tenth as needed.) (e) Interpret the results. A. The expected number of questions answered correctly is 5.1 with a standard deviation of 0.04 B. The expected number of questions answered correctly is 3.7 with a standard deviation of 1.9 C. The expected number of questions answered correctly is with a standard deviation of 5.1 . D. The expected number of questions answered correctly is 5.1 with a standard deviation of 1.9 5. Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 39C3 6. A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a Three or four . (b) Compute the probability of randomly selecting Three or four or ten . (c) Compute the probability of randomly selecting a Seven or diamond. 7. Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. A newspaper finds that the mean number of typographical errors per page is eight . Find the probability that (a) exactly six typographical errors are found on a page, (b) at most six typographical errors are found on a page, and (c) more than six typographical errors are found on a page. (a) P(exactly six typographical errors are found on a page)equals (Round to four decimal places as needed.) (b) P(at most six typographical errors are found on a page)equals (Round to four decimal places as needed.) (c) P(more than six typographical errors are found on a page)equals (Round to four decimal places as needed.) Which of the events are unusual? Select all that apply. A. The event in part (a) is unusual. B. The event in part (b) is unusual. C. The event in part (c) is unusual. D. None of the events are unusual. 8. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n equals 80 p equals 0.6 The mean, mu is 48 round to nearest tenth . The variance, 02sigma squared , is . (Round to the nearest tenth as needed.) The standard deviation, Sigma 0 , is . 8. A company that makes cartons finds that the probability of producing a carton with a puncture is 0.05 , . Answer parts (a) and (b) below. (a) Are the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" mutually exclusive? Explain. A. Yes, a carton can have a puncture and a smashed corner. B. Yes, a carton cannot have a puncture and a smashed corner. C. No, a carton can have a puncture and a smashed corner. D. No, a carton cannot have a puncture and a smashed corner. (b) If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed corner. The probability that a carton has a puncture or a smashed corner is . (Type an integer or a decimal. Do not round.) 9 Use the frequency distribution, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the 18 to 20 years old age range. Response 18 to 20 4.4 21 to 24 8.2 25 to 34 23.5 35 to 44 25.6 45 to 64 54.5 Frequency 65 or over 28.2 The probability that a voter chosen at random is in the 18 to 20 years old age range is 10. Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.00 1 0.00 2 1.00 3 0.00 4 0.00 A yes because the probabilities sum to 1 and are all bet 0 and 1 inclusive B no, because some of the probabilities have values greater tjam 1 and less than o C yes, because the distribution is symmetric D no, because the total probability is not equal to 1