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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
Standard deviation = =
=
= 1.68
(b) Probability that 10 of the problems can be resolved today = P(X = 10)
P(X = 10) =
= = 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
(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