7. 16 points DevoreStat9 3.E.013 A mail-order company business has six telephone

Question

7. 16 points DevoreStat9 3.E.013 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. p(x) 0.11 0.15 0.20 0.250.190.06 0.04 Calculate the probability of each of the following events (a) fat most three lines are in use (b) fewer than three lines are in use (c) at least three lines are in use (d) fbetween two and five lines, inclusive, are in useh (e)between two and four lines, inclusive, are not in use) (f) (at least four lines are not in use} Need Help? tTalk to a Tuter Talk to a Tutor

Explanation / Answer

a)

P( X <= 3) = P( X = 0) + P( X = 1) + P( X = 2) + P( X = 3)

= 0.11 + 0.15 + 0.20 + 0.25

= 0.71

b)

P( X < 3) = P( X <= 2)

= P( X = 0) + P( X = 1) + P( X = 2)

= 0.11 + 0.15 + 0.20

= 0.46

c)

P( X >= 3) = P( X = 3) + P( X = 4) + P( X = 5) + P( X = 6)

= 0.25 + 0.19 + 0.06 + 0.04

= 0.54

d)

P( 2 <= X <= 5) = P( X = 2) + P( X = 3) + P( X = 4) + P( X = 5)

= 0.20 + 0.25 + 0.19 + 0.06

= 0.70

e)

P( 4 >= X >= 2) = P( x = 2) + P( X = 3) + P( X = 4) }

= 0.20 + 0.25 + 0.19

= 0.64

f)

P(At least 4 lines are not in use) = P( At most 2 lines are in use)

= P( X <= 2)

= P( X = 0) + P( X = 1) + P( X = 2)

= 0.11 + 0.15 + 0.20

= 0.46

(Since there are 6 lines, if at least 4 lines are not in use then remaining 2 lines should be in use)

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