A mailorder company business has six telephone lines Let X d

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.

Calculate the probability of each of the following events. (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 not in use}


(f) {at least four lines are not in use}

Solution

You have the pdf ( probability density function ) so you almost have the answer for all the questions

a)

at most 3 lines are in use that means that can be fewer than 3 but no more than 3

P=0.10+0.15+0.20+0.25 = 0.7

b)

fewer than 3 that means x=0+ x=1 + x=2

P=0.10+0.15+0.20 = 0.45

c)

at least 3 lines are in use

that means minimun 3 are in use , it can be more so

P = 0.25 +0.20 +0.05+0.05 = 0.55

d)

between 2 and 5 lines are in use

that means x=2 + x=3 + x=4 + x=5

P= 0.20+0.25+0.20+0.05 = 0.7

e)

between 2 and 4 lines but these are not use

that probability is the same that 1 - [ are in use in that interval]

P= 1-[0.20+0.25+0.20] = 0.35

f)

at least 4 lines are not in use that means that at most 3 lines are in use is the same

0.7