MATH 1131 3.0 (2014 Fall)Assignment 1(Due Date: October 15, 2014)Question 1: In the provided EXCEL ﬁle is the data set of incarceration rates (prisoners per100,000 of nation’s population) for 217 nations of the world, according to the World PrisonBrief at the International Centre for Prison Studies.a. Use any software and obtain the histogram for this data set.b. How would you describe the overall shape of this data set? Do you suspect any outlyinggroup in this data set?c. Report the sample mean and sample standard deviation?d. Is the Empirical Rule applicable to this data set? Why or why not?e. Regardless of your answer in part (d), apply the Empirical Rule to this data set.What percentage of data falls within two standard deviation of the mean? What doesEmpirical Rule said this value should be?f. Report the 5 number summary of this data set. (Note: Don’t use software. Use themethod discussed in class.)g. Based on the result in part (f), sketch the modiﬁed boxplot.Question 2: A survey of students in a large Introductory Statistics class asked about theirbirth order (1 = “oldest or only child”; 2 = others) and which faculty of the university theywere studying under. Here are the data:BirthFaculty1Arts and Sciences 34Agriculture52Human Ecology15Other12Order223412818a. Is we select a student at random, what is the probability that the person is an Artsand Sciences student who is not “oldest or only child”?b. Among the Arts and Sciences students, what is the probability that a student was the“oldest or only child”?c. What is the probability that an “oldest or only child” is enrolled in the AgricultureFaculty?d. What is the probability that a randomly selected student is either the “oldest or onlychild” or enrolled in the Faculty of Human Ecology?1Question 3: At Elmo’s, an old-fashioned barber shop in Florida, 70% of all customers gota haircut, 40% got a shave, and 15% get both.a. What is the probability that a randomly selected customer gets a shave or a haircut?b. What is the probability that a randomly selected customer gets only a shave?c. What is the probability a randomly selected customer get a shave, given they get ahaircut?d. Are haircut and shave independent events? Why?e. Are haircut and shave disjoint (mutually exclusive) events? Why?Question 4: An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume eachshot is independent of the others. If she shoots six arrows, what is the probability of eachof the following results?a. Her ﬁrst bull’s-eye comes on the third arrow.b. She gets exactly four bull’s-eye out of her 6 arrows.c. She gets at least four bull’s-eye out of her 6 arrows.d. She misses the bull’s-eye at least once.e. She gets her fourth bull’s-eye at her ﬁnal shot.Question 5: According to AAA Repair LTD, the number of repair calls that an appliancerepair shop may receive during an hour:Repair CallsProbability00.110.320.430.2a. How many calls should the shop expect per hour?b. What is the standard deviation?c. During an eight-hour work day, how many calls should the shop expect? What is thecorresponding standard deviation?Question 6: The waist size of Canadian males is reported to be normally distributed witha mean of 36.33 inches and a standard deviation of 4.02 inches.a. A Canadian man is randomly selected. What is the probability that his waist size isless than 38 inches?2b. What is the waist size that is exceeded by 90% of North American males?c. A Canadian male is randomly selected. What is the probability that his waist size isexactly 36.33 inches?d. 10 Canadian men are randomly selected. What is the probability that at most 8 ofthem has waist size over 38 inches?