A brand name has a 50 recognition rate Assume the owner of t

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 8 randomly selected consumers.

What is the probability that AT LEAST 7 of the selected consumers recognize the brand name?

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where     
k = number of successes in trials        
n = is the number of independent trials        
p = probability of success on each trial

P( X = 7 ) = ( 8 7 ) * ( 0.5^7) * ( 1 - 0.5 )^1
= 0.0313

P( X = 8 ) = ( 8 8 ) * ( 0.5^8) * ( 1 - 0.5 )^0
= 0.0039

P( X > = 7 ) = P( X = 8 )+ P( X = 7 ) = 0.0352