RYERSON UNIVERSITY FACULTY OF ENGINEERING, ARCHITECTURE & SCIENCE

DEPARTMENT OF CHEMICAL ENGINEERING

CHE 331 Engineering Statistical Design

Assignment # 1 (Due on Jan. 27, 2015)

Problem # 1 In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that six of the tanks contain material in which the viscosity exceeds customer requirements.

a) What is the probability that exactly one tank in the sample contains high viscosity material?

b) What is the probability that at least one tank in the sample contains high viscosity material?

c) In addition to the six tanks with high viscosity levels, four different tanks contain material with high impurities. What is the probability that exactly one tank in the sample contains high viscosity material and exactly one tank in the sample contains material with high impurities?

Problem # 2 A real estate agent is showing homes to a prospective buyer. There are ten homes in the desired price range listed in the area. The buyer has time to visit only four of them.

a) In how many ways could the four homes be chosen if the order of visiting is considered?

b) In how many ways could the four homes be chosen if the order is disregarded? Problem # 3 Student Engineers Council at an Indiana college has one student representative from each of the five engineering majors (civil, electrical, industrial, materials, and mechanical). In how many ways can

a) Both a council president and a vice president be selected? b) A president, a vice president, and a secretary be selected? c) Two members be selected for the President’s Council?

Problem # 4 The rise time of a reactor is measured in minutes (and fractions of minutes). Let the sample space be positive, real numbers. Define the events A and B as follows: A = { x | x <72.5 } B = { x | x > 52.5 } Describe each of the following events:

a) A' b) B' c) A ∩ B d) A ∪ B