A brand name has a 40 recognition rate Assume the owner of

A brand name has a 40 % recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 7 randomly selected consumers. Compute parts (a) through (b).

A) What is the probability that all of the selected consumers recognize the brand name?

B) What is the probability that at least 3 of the selected consumers recognize the brand name?

Solution

a)

P(all) = 0.4^7 = 0.0016384 [answer]

b)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    7      
p = the probability of a success =    0.4      
x = our critical value of successes =    3      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   2   ) =    0.419904
          
Thus, the probability of at least   3   successes is  
          
P(at least   3   ) =    0.580096 [answer]