Superlesson
Project 6-2
Advanced Algebra
Chapter 6, Counting and Arranging Discrete Objects
Each year, the National Institute of Standards and Technology, a U.S. government agency, presents the Malcolm Baldrige National Quality Award to one or more U.S. companies for excellence and quality achievement.
Part A, Combinations
1. Granite Rock Company won a Baldrige Award in 1992.
a. Write an expression nCr which could be evaluated to find the number of ways 5-member quality teams can be chosen from among all of Granite Rock's employees.
b. The reliability of several Granite Rock processes has reached the six-sigma level. What is the probability that a given step in one such process will be defective?
c. Solectron Corporation won a Baldrige Award in 1991. How many ways could the number of superior performance awards that the company won in 1990 be chosen from all of the awards it has won in the past 10 years?
Part C, Making Connections
2 . Wainwright Industries won a Baldrige Award in 1994.
a. Find Wainwright's rate of overall customer satisfaction since 1992 and express it as a decimal.
b. The probability that a number of customers in a group will be satisfied with a company's performance can be modeled by the binomial (dx + sy)n, where d is the rate of customer dissatisfaction, s is the rate of customer satisfaction, and n is the number of customers in the group. Write the binomial for a group of five Wainwright Industries customers.
c. Expand the binomial.
d. The probability that exactly a customers in a group of n customers are dissatisfied is given by the coefficient of xay n - a in the binomial expansion of (dx + sy) n. Find the probability that, in a randomly chosen group of five Wainwright customers, at least three are dissatisfied.