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SOC 2105 TUTOTRIAL WORKSHEETSemester 1 2015/2016Ms. Shameza DavidThe following data give the numbers of car thefts that occurred in a city during the past 12 days.6 3 7 11 4 3 8 7 2 6 9 15Find the mean, median, and mode.The following data give the revenues (in millions of dollars) for the last available fiscal year for a sample of six charitable organizations for serious diseases (Charity Navigator, 2009). The values are, listed in order, for the Alzheimer’s Association, the American Cancer Society, the American Diabetes Association, the American Heart Association, the American Lung Association, and the Cystic Fibrosis Foundation.952 1129 231 668 49 149Compute the mean and median. Do these data have a mode? Why or why not?The following data give the number of shoplifters apprehended during each of the past 8 weeks at a large department store.7 1 08 3 1 51 26 1 1a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero?b. Calculate the range, variance, and standard deviation.The following data give the prices of seven textbooks randomly selected from a university bookstore.$89 $170 $104 $113 $56 $161 $147a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero?b. Calculate the range, variance, and standard deviation. The following data give the numbers of car thefts that occurred in a city in the past 12 days.6 3 7 1 14 3 8 7 2 6 9 1 5Calculate the range, variance, and standard deviation. Two students are randomly selected from a statistics class, and it is observed whether or not they suffer from math anxiety. How many total outcomes are possible? Draw a tree diagram for this experiment.Draw a Venn diagram.A test contains two multiple-choice questions. If a student makes a random guess to answer each question, how many outcomes are possible? Depict all these outcomes in a Venn diagram. Also draw a tree diagram for this experiment. (Hint: Consider two outcomes for each question—either the answer is correct or it is wrong.)A box contains a certain number of computer parts, a few of which are defective. Two parts are selected at random from this box and inspected to determine if they are good or defective. How many total outcomes are possible? Draw a tree diagram for this experiment.In a group of people, some are in favor of a tax increase on rich people to reduce the federal deficit and others are against it. (Assume that there is no other outcome such as “no opinion” and “do not know.”). Three persons are selected at random from this group and their opinions in favor or against raising such taxes are noted. How many total outcomes are possible? Write these outcomes in a sample space S. Draw a tree diagram for this experiment.In a group of adults, some have iPods, and others do not. If two adults are randomly selected from this group, how many total outcomes are possible? Draw a tree diagram for this experiment. List all the outcomes included in each of the following events. Indicate which are simple and which compound events are.a. One person has an iPod and the other does not.b. At least one person has an iPod.c. Not more than one person has an iPod.d. The first person has an iPod and the second does not.Suppose a randomly selected passenger is about to go through the metal detector at JFK Airport in New York City. Consider the following two outcomes: The passenger sets off the metal detector, and the passenger does not set off the metal detector. Are these two outcomes equally likely? Explain why or why not. If you are to find the probability of these two outcomes, would you use the classical approach or the relative frequency approach? Explain why.Thirty-two persons have applied for a security guard position with a company. Of them, 7 have previous experience in this area and 25 do not. Suppose one applicant is selected at random. Consider the following two events: This applicant has previous experience, and this applicant does not have previous experience. If you are to find the probabilities of these two events, would you use the classical approach or the relative frequency approach? Explain why.The president of a company has a hunch that there is a .80 probability that the company will be successful in marketing a new brand of ice cream. Is this a case of classical, relative frequency, or subjective probability? Explain why.The coach of a college football team thinks that there is a .75 probability that the team will win the national championship this year. Is this a case of classical, relative frequency, or subjective probability? Explain why.A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is a. red? b. green?A die is rolled once. What is the probability that a. a number less than 5 is obtained? b. a number 3 to 6 is obtained? Let x be the number of errors that appear on a randomly selected page of a book. The following table lists the probability distribution of x.x 0 1 2 3 4P(x) .73 .16 .06 .04 .01Find the mean and standard deviation of x.Let x be the number of magazines a person reads every week. Based on a sample survey of adults,the following probability distribution table was prepared.x 0 1 2 3 4 5p(x) .36 .24 .18 .10 .07 .05Find the mean and standard deviation of x.The following table gives the probability distribution of the number of camcorders sold on a given day at an electronics store.Camcorders sold 0 1 2 3 4 5 6Probability .05 .12 .19 .30 .20 .10 .04Calculate the mean and standard deviation for this probability distribution. Give a brief interpretation of the value of the mean.The following table, reproduced from Exercise 5.12, lists the probability distribution of the number of patients entering the emergency room during a 1-hour period at Millard Fellmore Memorial Hospital.Patients per hour 0 1 2 3 4 5 6Probability .2725 .3543 .2303 .0998 .0324 .0084 .0023Calculate the mean and standard deviation for this probability distribution.Let x be a discrete random variable that possesses a binomial distribution. Using the binomial formula,find the following probabilities.a. P(x = 0) for n = 5 and p = .05b. P(x = 4) for n = 7 and p = .90c. P(x = 7) for n = 10 and p = .60A professional basketball player makes 85% of the free throws he tries. Assuming this percentage will hold true for future attempts, find the probability that in the next eight tries, the number of free throws he will make isexactly 8 b. exactly 5Love Stinks? J. Fetto, in the article “Love Stinks” (American Demographics, Vol. 25, No. 1, pp. 10–11), reports that Americans split with their significant other for many reasons—including indiscretion, infidelity, and simply “growing apart.” According to the article, 35% of American adults have experienced a breakup at least once during the last 10 years. Of nine randomly selected American adults, find the probability that the number, X, who have experienced a breakup at least once during the last 10 years isa. exactly five; at most five; at least five.b. at least one; at most one.c. between six and eight, inclusive.23. Gestation Periods. The probability is 0.314 that the gestation period of a woman will exceed 9 months. In six human births, what is the probability that the number in which the gestation period exceeds 9 months isa. exactly three?b. exactly five?c. at least five?d. between three and five, inclusive? ................
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