Question

A mail-order computer software business has six telephone lines. Let x denote the number of lines in use at a specified time. The probability distribution of x is as follows:

X P(x)

0 0.11

1 0.17

2 0.20

3 0.25

4 0.15

5 0.08

6 0.04

Calculate the probability of:

(a). at most three lines are in use.

(b). fewer than three lines are in use.

(c). at least three lines are in use.

(d). between two and five lines (inclusive) are in use.

(e). between two and four lines (inclusive) are in use.

(f.) at least one line is not in use.

how do I even set the equation up? :(

TIA!

(c). at least three lines are in use.

(d.) between two and five lines (inclusive) are in use.

(e). between two and four lines (inclusive) are in use.

(f). at least one line is not in use.

Answer 1

a)

Required probability = P(at most 3 lines are in use) =

b)

Required probability = P(fewer than 3 lines are in use) =

c)

Required probability = P(at least 3 lines are in use) =

d)

Required probability = P(between two and five lines (inclusive) are in use) =

e)

Required probability = P(between two and four lines (inclusive) are in use) =

f)

Required probability = P(at least one line is not in use) =