SOLUTION: A brand name has a 60​% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 6 randomly selected consumers. What

Algebra ->  Probability-and-statistics -> SOLUTION: A brand name has a 60​% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 6 randomly selected consumers. What       Log On


   

Question 1086135: A brand name has a 60​% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 6 randomly selected consumers.
What is the probability that exactly 5 of the selected consumers recognize the brand​ name?

. What is the probability that all of the selected consumers recognize the brand​ name?
What is the probability that at least 5 of the selected consumers recognize the brand​ name?
If 66 consumers are randomly​ selected, is 55 an unusually high number of consumers that recognize the brand​ name?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Exactly 5 is 6C5 (6 ways to choose them) (.6)^5*.4=6*.0311=0.187
All of them is 0.6^6=0.047
at least 5 is the sum of the first two or 0.234
Can do it with normal approximation or binomial
binomial is 66C55*.6^55*.4^11=0.000028
normal has mean of 66*0.6=39.6
sd is sqrt (66*0.6*0.4)=sqrt(15.84)=3.98
do it greater than 54.5 for continuity correction.
z>=(54.5-39.6)/3.98>=+3.74
This probability is 0.00009.
Yes, it would be an unusually high number of consumers.