Question

In the mid-1990s, Colgate-Palmolive developed a new toothpaste for the U.S. market, Colgate Total, with an antibacterial ingredient that was already being successfully sold overseas. At that time, the word antibacterial was not allowed for such products by the Food and Drug Administration (FDA). In response, the name “Total” was given to the product in the United States. The one word would convey that the toothpaste is the “total” package of various benefits. Young & Rubicam developed several commercials illustrating Total’s benefits and tested the commercials with focus groups. One commercial touting Total’s long-lasting benefits was particularly successful. The product was launched in the United States in January of 1998 using commercials that were designed from the more successful ideas of the focus group tests. Suppose 32% of all people in the United States saw the Total commercials. Of those who saw the commercials, 40% purchased Total at least once in the first 10 months of its introduction. According to U.S. Census Bureau data, approximately 20% of all Americans were in the 45-64 age category. Suppose 24% of the consumers who purchased Total for the first time during the initial 10-month period were in the 45-64 age category. Within three months of the Total launch, Colgate-Palmolive grabbed the number one market share for toothpaste. Ten months later, 21% of all U.S. households had purchased Total for the first time. The commercials and the new product were considered a success. During the first 10 months of its introduction, 43% of those who initially tried Total purchased it again.   

1. What percentage of U.S. households purchased Total at least twice in the first 10 months of its release?

2. Can you conclude the initial purchase of Total was independent of age? Use a quantitative argument to justify your answer.

3. Calculate the probability that a randomly selected U.S. consumer is either in the 45-64 age category or purchased Total during the initial 10-month period.

4. What is the probability that a randomly selected person purchased Total in the first 10 months given that the person is in the 45-64 age category?

e. What percentage of people who did not see the commercials purchased Total at least once in the first 10 months of its introduction?

Answer 1

(1) So the review expresses that 21% of all families bought the product for the first time
  
43% of this obtained it againin a similar timespan so the level of US families who

purchased it twice is 0.430.21= 0.09 = 0.09/100 =9%

Thus from the above 9% of all the US family units acquired it twice

(2) Now 20% of all americans are in the 45-64 age gathering the product for the first time

24% of the shoppers who obtained out of the blue were in the 45-64 age gathering

and 0.240.21X = 0.05X were 45-64 age who acquired and 0.20X is the total populace of all

45-64 age gatherings

if X is the entire poplulation

This implies 5 out of 20 individuals in the 45-64 age gathering acquired aggregate for the first

time, henceforth age assemble is not independent of initial purchase.

(3) So 21 individuals in 100 acquired Total for the first as indicated by the review if 100 is the total population and according to Q2 5 individuals out of these were in the 45-64 age gathering

So likelihood that a randomly choosen individual bought aggregate in the initial 10 months given that he is in the 45-64 age gathering =5 individuals/21 individuals = 5/21 = 0.238.