During the early stage of product development, some companies use focus groups to get the reaction of

customers to a new product or design. The particular focus group in this example has nine randomly

selected customers. After being shown a prototype, they were asked to$,$Would you buy this product if it

was sold for Tsh $100,000.$ The questionnaire allowed only two answers yes or no$.$ When the answers were

totaled six of the nine customers in the group answered yes. Prior to the focus group the development team

claimed that $80\%$ of customer would want to buy the product at this price. If the developers are right, what

should we expect to happen at the focus group?

a$)$ Is it likely for six out of nine customers in the group to say they would buy it$?$

b$)$ What is the likelihood of the group to be unanimous?

c$)$ What assumptions are required for the answer in part b to be valid