Answer to Question #304371 in Statistics and Probability for jana

Question

A TELCO office has seven telephone lines. For the past months, the probability distribution of the random variable X which represents the number of busy lines per day, X={0, 1, 2, 3, 4, 5, 6, 7} P(X)={.02, .27, .06, .22, .15, .04, .08, .16}, what is the probability that the number of busy telephone lines in a day is fewer than six but at least one?

Answer 1

Let X be a random variable representing the number of busy lines per day, then

$P(1≤X<6)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=0.27+0.06+0.22+0.15+0.04=0.74$