Tire and Auto Supply is considering a 2for1 stock split Befo

Tire and Auto Supply is considering a 2-for-1 stock split. Before the transaction is finalized, at least two-thirds of the 1,200 company stockholders must approve the proposal. To evaluate the likelihood the proposal will be approved, the CFO selected a sample of 18 stockholders. He contacted each and found 14 approved of the proposed split. What is the likelihood of this event, assuming two-thirds (0.6667) of the stockholders approve? (Round your final answer to 4 decimal places.) Probability

Solution

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 =    18      
p = the probability of a success =    0.6667      
x = the number of successes =    14      
          
Thus, the probability is          
          
P (    14   ) =    0.129446125 [ANSWER]