Answer:
(a) 11.25 and 1.68  
(b) 0.1651
(c) 0.3903
(d) 0.6865
Step-by-step explanation:
We are given that GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 75% of the cases and suppose the 15 cases reported today are representative of all complaints. 
This situation can be represented through Binomial distribution as; 
 
 
where,  n = number of trials (samples) taken = 15 
              r = number of success
              p = probability of success which in our question is % of cases in 
                   which customer problems are resolved on the same day, i.e.;75% 
So, here X ~  
 
(a) Expected number of problems to be resolved today = E(X) 
             E(X) =  = n * p = 15 * 0.75 = 11.25
 = n * p = 15 * 0.75 = 11.25 
     Standard deviation =  =
 =  =
 =  = 1.68
 = 1.68
(b) Probability that 10 of the problems can be resolved today = P(X = 10) 
      P(X = 10) =  
 
                     =  = 0.1651
 = 0.1651
(c) Probability that 10 or 11 of the problems can be resolved today is given by = P(X = 10) + P(X = 11) 
     =  
 
     =  = 0.3903
 = 0.3903
(d) Probability that more than 10 of the problems can be resolved today is 
     given by = P(X > 10) 
P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)  
=  
 
 =  
 
 = 0.6865