An internal survey by a firm reveals that 56 percent of thei

An internal survey by a firm reveals that 56 percent of their customers rate their product as \"excellent.\" The firm contacts 5 additional customers. Calculate the probability that 3 or 4 of these customers rate the firm\'s product as \"excellent.\" Give you answer in decimal form and round your answer to three decimal places. Use the Binomial Probability Distribution function to solve

Solution

For x = 3:

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    5      
p = the probability of a success =    0.56      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.339992576

For x = 4:

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    5      
p = the probability of a success =    0.56      
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.216358912

Thus,

P(3 or 4) = 0.339992576 + 0.216358912 = 0.556351488 [ANSWER]