ADM2303 - Fall 2015 Section: A-G Assignment 2 - Part II Random Variables and Discrete and Continuous Distributions Total points : 20 Do not forget to include a statement of academic integrity within the statement that you provide in the answer area to part II. Finally, note that you are required to show your work for full credit correct numeric answers may earn you little credit unless you show your work. Assignments are to be converted to PDF format and uploaded to Blackboard Learn on or before the due date.[DUE DATE October 23rd] Question 1.(7 points) Consider a small bike shop in Bank Street Ottawa. Bicycles arrive at the shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take: The times for each setup phase are independent. The means and standard deviations of the times (in minutes) are as shown: Phase Unpacking Assembly Tuning Mean 3.5 21.8 12.3 SD 0.7 2.4 2.7 (a) What are the mean and standard deviation for the total bicycle setup time ? (1 point) (b) A customer decides to buy a bike like one of the display models but wants a dierent color. The shop has one, still in the box. The manager says that they can have it ready in half an hour. Do you think the bike will be set up and ready to go as promised ? (Hint: Base your decision on the expected value) (1 point) (c) Most days, the bike shop completes this process on three bikes. The manager schedules 90 minutes per day in total for store employees to complete this task. Are the workers going to be able to complete this task in 90 minutes (of their combined work times)? (Hint: Base your decision on the expected value)(1 point) The bike shop will be oering two specially priced children's models at a sidewalk sale. The basic model will sell for $120 and the deluxe model for $150. Past experience indicates that sales of the basic model will have a mean of 5.4 bikes with a standard deviation of 1.2, and sales of the deluxe model will have a mean of 3.2 bikes with a standard deviation of 0.8 bikes. The cost of setting up for this sidewalk sale is $200. (d) Dene appropriate random variables and use them to express the bicycle shop's net income. (1 point) (e) What is the mean of the net income ?(1 point) (f) What is the standard deviation of the net income ? (1 point) (g) Do you need to make any assumptions in calculating the mean? How about the standard deviation ?(1 point) 1 ADM2303 - Fall 2015 Section: A-G Question 2.(4 points) According to Neurological research study published in Science news (161 no.24, 2002), in about 80% of people, language abilities reside in the brain's left side. Another 10% display right-brain language centres, and the remaining 10% have two sided language control. The later two groups are categorized as mainly lefthanders. (a) Assume that a rst-year composition class in Telfer contains 25 randomly selected students. What is the probability that more than 22 of these students have only left-brain language control ?(1 point) (b) In a randomly assigned group of ve of these students, what is the probability that no one has two sided language control ? (1 point) (c) In the entire rst year class of 1200 students, how many would you expect to nd of each type ? (1 point) (d) In the entire rst year class of 1200 students, what are the mean and standard deviation of the number of these students who will be right-brained in language abilities ? (1 point) Question 3.(5 points) In an island in pacic ocean, almost every year there is some incidence of volcanic activity. In 2007, there were ve volcanic episodes, dened as either eruptions or, sizable seismic activity. Suppose the mean number of episodes is 2.4 per year. Let Y be the number of episodes in the two-year period 2011-2013. (a) What model might you use to model Y ?(1 point) (b) What is the mean number of episodes in this period ?(1 point) (c) What is the probability that there will be no episodes in this period ?(1 point) (d) What is the probability that there are more than three episodes in this period ?(2 points) Question 4.(4 points) The length of human pregnancy from conception to birth can be modeled as a distribution that is approximately normal with mean 266 days and standard deviation 16 days. (a) According to this model, what percentage of human pregnancies last longer than 279 days? (2 points) (b) Approximately 7 % of infants are premature. Using this model, nd the pregnancy time that would result in a premature birth. (2 points) 2