Question

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 80% of the cases. Suppose the 14 cases reported today are representative of all complaints.

1.) What is the probability 10 or 11 of the problems can be resolved today?

2.) What is the probability more than 9 of the problems can be resolved today?

Answer 1

BIONOMIAL 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 (a) N=14, p=0.80, X=10 P(X= 10 ) = ( 14 10 ) * (0.8^10) * (1 - 0.8 )^4 = 0.17197 N=14, p=0.80, X=11 P( X = 11 ) = ( 14 11 ) * (0.8^11) * (1 - 0.8)^3 = 0.250139 probability 10 or 11 of the problems can be resolved today = P(X = 10 ) + P(X = 11 ) = 0.17197 + 0.250139 = 0.422109 (b) probability more than 9 of the problems can be resolved today P(X< = 9) = P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) = (14 9) * 0.8^9* (1-0.8) 45+ (148 ) * 0.848*(1-0.8) 46+ (14 7) * 0.8^7* (1-0.8) ^7 + (14 6 ) * 0.8^6* (1-0.8) 48 + (145) * 0.8^5 * ( 1-0.8) ^9+ (14 4) * 0.8^4 * ( 1-0.8) 410 + (14 3) * 0.8^3 * ( 1-0.8) ^11 + ( 14 2) * 0.8^2 * ( 1-0.8 ) ^12 + ( 14 1) * 0.8^1 * ( 1-0.8) 413 + ( 14 0) * 0.840 * ( 1-0.8) 414 = 0.12984 P(X> 9) = 1 - P(X<=9) = 1 -0.12984 = 0.87016