Question

A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.

x 0 1 2 3 4 5 6
p(x) 0.10 0.15 0.20 0.25 0.20 0.05 0.05
Calculate the probability of each of the following events.

(a) {at most three lines are in use}

Answer 1

To calculate the probability of at most three lines being in use, we need to sum the probabilities of 0 lines, 1 line, 2 lines, and 3 lines being in use.

Step-by-step explanation:

To calculate the probability of at most three lines being in use, we need to sum the probabilities of 0 lines, 1 line, 2 lines, and 3 lines being in use.

1. P(0 lines) = 0.10
2. P(1 line) = 0.15
3. P(2 lines) = 0.20
4. P(3 lines) = 0.25

Adding up these probabilities, we get:

P(at most three lines are in use) = P(0 lines) + P(1 line) + P(2 lines) + P(3 lines) = 0.10 + 0.15 + 0.20 + 0.25 = 0.7, or 70%.