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 70% of the cases. Suppose the 14 cases reported today are representative of all complaints.
a-1. How many of problems would you expect to be resolved today? (Round your answer to 2 decimal places.)
a-2. What is the standard deviation? (Round your answer to 4 decimal places.)
What is the probability 8 of the problems can be resolved today? (Round your answer to 4 decimal places.)
What is the probability 8 or 9 of the problems can be resolved today? (Round your answer to 4 decimal places.)
What is the probability more than 9 of the problems can be resolved today? (Round your answer to 4 decimal places.)
a-1)
E(X) = n * p = 14 * 0.70 = 9.8
a-2)
Standard deviation = sqrt [ np(1-p) ]
= sqrt [ 14 * 0.70 * 0.30 ]
= 1.7146
b)
X ~ Binomial (n,p)
Where n = 14 , p = 0.70
P(X) = ^{n}C_{x} p^{x} (1-p)^{n-x}
P( X = 8) = ^{14}C_{8} 0.70^{8} 0.30^{6}
= 0.1262
c)
P( X = 8 or 9) = P (X = 8) + P (X = 9)
= ^{14}C_{8} 0.70^{8} 0.30^{6} +^{14}C_{9} 0.70^{9} 0.30^{5}
= 0.1262 + 0.1963
= 0.3225
d)
P( X > 9) = P( X >= 10)
= P( X = 10) + P( X = 11) + P( X = 12) + P( X = 13) + P( X = 14)
= ^{14}C_{10} 0.70^{10} 0.30^{4} +^{14}C_{11} 0.70^{11} 0.30^{3} +^{14}C_{12} 0.70^{12} 0.30^{2} +^{14}C_{13} 0.70^{13} 0.30^{1} +^{14}C_{14} 0.70^{14} 0.30^{0}
= 0.5842
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