Question

2.2   

The following information is based on the trends in the United States published by the Food Marketing Institute, Washington, D.C. The columns represent length of customer loyalty (in years) at a primary supermarket. The rows represent regions in United States

			Loyalty
Region	Less than a ye1-ar	1-2 years	3-4 years	5-9 years	10-14 years	15 or more years	Row total
East	32	54	59	112	77	118	452
Midwest	31	68	68	120	63	173	523
South	53	92	93	158	106	158	660
West	41	56	67	78	45	86	373
Column total	157	270	287	468	291	535	2008

What is the probability that a customer chosen at random

1. has been loyal 10 to 14 years?                                                                                   [1]
2. has been loyal at least 10 years?                                                                                [2]
3. has been loyal at least 10 years, given that he or she is from the west?                   [3]

2.3.     

Suppose that of all the products manufactured at ZOYAZA factory, 30% come from machine 1, 25% from machine 2, and the remainder from machine 3. It is well known that 8% of machine 1 products are defective, 12% of machine 2 products are defective, and 10% of machine 3 products are defective.

2.3.1    If one product can be randomly selected from ZOYAZA factory warehouse, what is the probability that it will be defective?                                                                             [2]

2.3.2    A quality control inspector has just randomly selected one product from ZOYAZA factory warehouse and has found it to be defective. What is the probability that it was produced by machine 2 or machine 3?                                                                        [4]                   

Answer 1

2.2)

[1] The probability that a customer chosen at random has been loyal 10 to 14 years = 291/2008 = 0.1449

[2] The probability that a customer chosen at random lt has been loyal atleast 10 years = (157 + 270 + 287 + 468)/2008

= 1182/2008 = 0.5886

[3] The required probability = (41 + 56 + 67 + 78)/373

= 242/373 = 0.6488

2.3)

2.3.1) The required probability = 0.30*0.08 + 0.25*0.12 + 0.45*0.10

= 0.099

2.3.2) The required probability = (0.25*0.12 + 0.45*0.10)/0.099

= 0.7576