E. Wasil ITEC 610 Class Assignment 1 Show all work. Allow 90 minutes. Name: Question 1 2 3 4 Total Points 1 1. (15 points) Data Analysis Using Descriptive Statistics Two different machines at Eagle Mills fill boxes with bran flakes cereal. The quality control manager has set a target weight of the contents of a filled box at 24 ounces. To check the performance of each machine, the manager randomly samples 15 boxes filled by each machine in a single production run and weighs the contents. The data set from a recent production run follows. Box Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Machine Number 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Weight of Contents (ozs) 24.02 23.89 24.11 24.06 23.81 23.87 23.88 24.02 24.06 23.96 23.91 23.98 24.02 23.98 23.90 Box Number 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Machine Number 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Weight of Contents (ozs) 23.94 23.88 24.11 24.05 24.02 23.90 24.07 24.07 24.04 23.99 24.10 24.01 24.14 23.91 24.03 a. (10 points) Fill in the chart below. Show your work on the reverse side of this page. Machine 1 Machine 2 Mean Median Mode Range Standard Deviation b. (5 points) Each machine is supposed to fill boxes with a target weight of 24 ounces. How is each machine performing with respect to this standard? Be sure to use the statistical measures that you reported in part a. to answer this question. 2 2. (15 points) Probability Eagle Manufacturing is a mid-size company that recently conducted a survey of its employees to determine their attitudes toward a buyout of the company's stock. The company's 1,040 employees were asked whether they favored a buyout and when they were planning to retire. Their responses are given in the table below. Favor Buyout Yes No <5 140 60 plan to retire in (years) 5 15> 15 75 179 122 464 Suppose that one of the surveyed employees is selected at random. Using this data set, find the following probabilities. a. (3 points) The employee does not favor a buyout. b. (3 points) The employee plans to retire in more than 15 years. c. (3 points) The employee favors a buyout or plans to retire in 5 to 15 years. d. (3 points) Given that the employee plans to retire in less than 5 years, the employee does not favor the buyout. e. (3 points) Let A be the event that the employee favors the buyout. Let B be the event that the employee plans to retire in more than 15 years. Are A and B independent? Explain. 3 3. (10 points) Probability 3.1 (5 points) Eagle Computers manufactures portable disk drives. Eagle knows that a shipment of 30 disk drives sent to a large discount store contains eight defective drives. Eagle also knows that the store will choose two of the drives at random, test them, and accept the shipment if both drives are not defective. What is the probability that the shipment is accepted? 3.2 (5 points) Eagle Nursery advertises that is has 10 elm trees for sale. Unknown to the nursery, three of the trees have already been infected with Dutch elm disease and will die within a year. If a buyer purchases two trees at random from the lot, what is the probability that both trees will be healthy? That at least one of the trees is infected? 4 4. (10 points) Discrete Random Variable Six people apply for two identical positions in a company. Four are minority applicants and the remainder are nonminority. All the applicants are equally qualified and the choice is therefore a random selection of two applicants from the six available. Let the random variable X = number of minority applicants chosen, where x = 0, 1, 2. Construct the probability distribution of X. Find E(X) and Var (X)