A brand name has a 50% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 7 randomly selected consumers.A) What is the probability that exactly 6 of the selected consumers recognize the brand name is ______? (Round to 3 decimal places)B) What is the probabilty that all the selected consumers recognize the brand _______?C) What is the probability that 3 of the selected consumers recognize the brand _______?D) If 4 consumers are randomly selected is 3 an unusually high number of consumers that recognize the brand name ______?

Answer:0.0547,0.0078,0.25Step-by-step explanation:Any random customer selected probability to recognize = 50% = 0.50 which remains the same for each customer.  Also there are only two outcomes.  Hence X the no of customers who recognize brand name is BinomialX is Bin (7,0.50)a) [tex]P(x=6) = 7C6 (0.5)^7 = 0.0547[/tex]b) [tex]P(X=7) = (0.5)^7 = 0.0078[/tex]c) [tex]P(X=3) = 7C3 (0.5)^7\\= 0.2734[/tex]d) Here n changes from 7 to 4.  But p probability for success remains the same.Hence [tex]P(X=3) = 4C3 (0.5)^4 = 0.25[/tex]This probability is not unusually high.If 4 consumers are randomly selected is 3 an unusually high number of consumers that recognize the brand name is 0.25