hw4 - Decide whether the graph represents a discrete random...

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Unformatted text preview: Decide whether the graph represents a discrete random variable or a continuous random variable. The annual snowfall at a summit pass in California ~—+-—~—: 2 2 ; :—+ 350 400 450 500 550 600 Choose the type of random variable represented in the graph. '3'” 3- Continuous random variable _ _ The graph represents a continuous random variable because 0 13' Discrete random variable the snowfall is a random variable that cannot be counted. Decide whether the random variable X is discrete or continuous. x represents the volume of water per minute from a showerhead. A discrete random variable has either a finite number of values or a countable number of values, where "countable" refers to the fact that there might be Is the random variable discrete or continuous? infinitely many values, but they can be associated with a counting process. A continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale in such a way that there 0 13. discrete are no gaps or interruptions. Q a- continuous Decide whether the random variable x is discrete or continuous. x represents the number of arrests made by a given police officer. Is the random variable discrete or continuous? D a. Continuous :33 in Discrete The variable is discrete because the number of arrests can be counted. In the following probability distribution, a sociologist surveyed the households in a small town. The random variable x represents the number of dependent children in the households. x 0 1 2 3 4 Pb!) 0.0? 0.22 0.35 ? 0.14 Determine the missing probability in this distribution. 0.22 (Round to the nearest hundredth.) Find the sum of the known probabilities and subtract from 1. The distribution for the possible results ofan experiment is given. x 0 l 3 T 8 P(x) 0.05 0.23 0.35 0.23 0.14 Which statement applies to the distribution? O a- This is not a probability distribution; the probabilities sum to more than 1. O h- This is not a probability distribution; the values ofx are not sequential integers. O C- This is not a probability distribution; the probabilities sum to less than 1. g [1- This is a probability distribution. Find the sum of the probabilities and determine which statement applies to the distribution. In an B-tam double-elimination tournament, the winning tam may play 4, 5, 6, or 7" games. Based on the results ofa large number of such tournaments, there is a probability of 01226 of winning in 4 games, 0.3255 ofwinning in 5, 0.3248 ofwinning in 6, and 0.2221 ofvvinningin? games. Tind the man number of games played by the winner ofan S-tam double-elimination oumament. 5.6414 games (Round to four decimal places.) Find the standard deviation of the probability distribution. 0.9641 games (Use an unrounded value of the man. Round to four decimal places.) Which of the statements applies? HINT: Consider the mean and standard deviation. 0 El- It is unusual foratarn to win in 5 games. © 13- It is not unusual for a team to win in 4 games. Usethe formula '0. = ExP[x] to findtheman. Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the fo owing probability distribution. x 0 0 r P(x) 0.01. . . . . 030014 What is the man of the distribution? 5.2 problems (Round to the narest hundredth.) What is the variance of the distribution? Use the unrounded value of the man to find your answer. 3.?6 problems (Round to four decimal places.) What is the standard deviation of the data? Use unrounded values to find your answer. 1.94 problems (Round to the narest hundredth.) What is the expected value of the data? 5.2 problems (Round to the narest hundredth.) To find the variance 0'2 ofx, use the formula. Multiply ach value of r by its corresponding probability and add the resulting products. 52 =2 [I- M2 P [I] USE the fommla for the Standard deviation J = N}; Eilféfijtlfsfiach value of): by 1ts corresponding probability and add the resulting The following probability distribution describes the number of do gs per household in a small town. x 0 1 2 3 4 5 P(x) 0.6493 0.2490 0.0634 0.0254 0.0088 0.0036 Jse this distribution to answer the following questions. What is the robability of randomly selecting a household that has fewer than four dogs? 0.9876 (Round to four decima. places.) What is the robability of randomly selecting a household that has at last three dogs? 0.0373 (Round to four decima. places.) What is the orobability of randomly selecting a household that has between one to four dogs? 0.3466 (Round to four decima. places.) Find the sum of the probabilities for those values of x warm-31.333 than four Find the sum of the probabilities for those values of): that are at last three. Find the sum of the probabilities for those values of): that are from one to four. Match the given probabilities with the correct graph. The histograms each represent binomial distributions. Each distribution has the same number of trials 31 but different probabilities of success p. p = 0.29,p = 0.95 ,p = 0.50 P [:cl' Which graph corresponds top = 0.29 ? Graph (Type a, b, or c.) Which graph corresponds to p =n_95 ? Graph E (Type a, b, or 3) Remember, a graph ofa binomial distribution with p > as is skewed left. The graph ofa binomial distribution withp < 0.5 is skewed right. The graph ofa Which graph corresponds top = 0.50? Graph E (Type a, b, or c.) binomial dismmmfln With}? = 0-5 is SYMME- Rernernber, a graph ofa binomial distribution withp :> 0.5 is skewed left. The graph ofa binomial distribution withp < 0.5 is skewed right. The graph ofa binomial distribution withp = 0.5 is symmetric. Remember, a graph of a binomial distribution with p > 0.5 is skewed left. The graph ofa binomial distribution withp < 0.5 is skewed right. The graph ofa binomial distribution withp = 0.5 is symmetric. Determine whether the experiment is a binomial experiment. Drawing a card from a deck with replacement 100 times and recording heartfnon-heart Cho os e the c orrect statement. O a. The experiment is not a binomia. experiment because the number of trials is not fixed. A binomial expm'mmt, is a prghahflity mm'mmt that satisfies all four ,3 b Th . . b. . . h th trial _ d d conditions I 8 experiment 15 not a mum' mpth amuse e S are not m span em' 1) there are a fixed number of trials where each trial is independent of the other 0 C The experiment is not a binomial experiment trials, I I because there are more than two possible outcomes for each trial. 2) the mildflm variable X 30111115 the 11111an 0f SUCCESSfUJ H1318, 3) there are only two possible outcomes for each trial, and E.) d- The Experiment iS a binomial expemnmt - 4) the probability of a success 13(5) is the same for each trial. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n=?5,p=0.3 he mean of binomial distribution. 22.5 (Round to the nearest tenth.) Find the variance of the binomial distribution. 03= (Round to the nearest hundredth.) Find ie standard deviation of the binomial distribution. or = 3.9? (Round to the nearest hundredth.) Usethe formua .u: =np,wheren=?5 andp = 0.3. Usetheformua o}=npq,wheren=?5,p=0.3,andq=l—p. Usethe formula CF =4“an,wheren=?5,p=0.3,andq=1—p. You are taking a multiple-choice quiz that consists of 4 questions. Each question has 3 possible answers, only one of which is correct. To complete the quiz, you randomly guess the answer to each question. F'nd the probability of guessing (a) exactly 3 answers correctly, (b) at least 3 answers correcty, or (c) less than 3 answers correctly. Find the probabiity of guessing exactly 3 answers correctly. 0.0988 (Round to four decimal places.) Find the probabiity of guessing at least 3 answers correctly. 0. l 1 11 (Round to four decimal places.) Find the probabLity of guessing less than 3 answers correctly. 0.8889 (Round to four decimal places.) Use the binomial probability formula. :1! _ ch3= scuff” = —.n"q’“ " [n — x) l x! Alternatively, use the binomialpdf function on a graphing calculator. Since P( x a 3) = P(3) + P(4), you need to find the two probabilities and add them. Use the fact that P(x «=: 3) = 1 - P(x 2 3). You could also use the binomialcdf function on a graphing calculator and then take the complement. Suppose that 65% of married couples paid for their honeymoon themselves. You randomly select 5 couples and ask each if they paid for their honeymoon themselves. Find the probability that the number of couples who say they paid for their honeymoon themselves is (a) exactly 3 couples, (b) more than 3 couples, and (c) at most 3 couples. Find the probability that exactly 3 couples say they pay for their honeymoon themselves. 0. 3364 (Round to four decimal places.) Find the probability that more than 3 couples say they paid for thier honeymoon themselves. 0.4284 (Round to four decimal places.) Find the probability that at most 3 couples say they paid for their honeymoon themselves. 0. 52' 1 6 (Round to four decimal places.) Use the binomial probability formula. In a binomial experiment, the probability of exactly x successes in n trials is x -3 ’1! x -x The probability that more than 3 couples said they paid for their own For} = ” Ox p q}: = [n —x] l :r! p q?! ' honeymoon, is found by finding the sum ofthe probabilities: P(4) + 13(5). Altmtively, use the binomialpdf fimctiun on a graphjng calculator Alternatively, use the binomialcdf function on a graphing calculator. To find the probabilities that at mo st 3 couples said they paid for their honeymoon, use the complementary rule. P(at most 3) = P(x 5 3) = 1 - (P(4) + P(S)). Thirty-eight percent of people in the United States have type O-positive blood. Five people are randomly selected and asked if their blood type is O-positive. Construct a probability distribution for the random variable x. Find the probabilities 13(0), F'(1), 13(2), 13(3), P(4), and F'(S). 13(0) = 0.092 (Round to the nearest thousandth.) P(l) = 0.281 (Round to the nearest thousandth.) 13(2) = 0.344 (Round to the nearest thousandth.) 13(3) = 0.211 (Round to the nearest thousandth.) 13(4) = 0.065 (Round to the nearest thousandth.) 13(5) = 0.008 (Round to the nearest thousandth.) se the binomial probability formula. * tematively, you could use the binomialde function on a graphing calculator. Assume the Poisson distribution applies. Use the mean to find the indicated probability. Find 13(3) when n =33. Pa) = (Round to the nearest thousandth.) Assume the Poisson distribution applies. Use the given mean .tt to find the indicated probability. Find H5) when n = 2.4. PcS>= (Round to the nearest thousandth.) Us ehte formula to find the probability of exactly 3: occurrences in an interval . it” 9‘“ P(x) — x I Decide which probability distribution - binomial, geometric, or Poisson - applies to the question. Given: The probability that a person will believe a rumor about the transgressions ofa certain politician is D35. Question: What is the probability that the eighth person to hear the rumor will be the first to believe it? Which probability distribution applies? 0 a. Binomial O b. Poisson Is used in problems Where you are interested in the umber of successes out ofn trials ls used in problems Where you are interested in the umber oftiials until the first success Is used in problems Where you are interested in the umber of occurrences that take place within a given unit of time Use the formula P[ ]= ...
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This note was uploaded on 04/01/2012 for the course MGQ 301 taught by Professor Orrange during the Fall '09 term at SUNY Buffalo.

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hw4 - Decide whether the graph represents a discrete random...

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