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An accounting office has six incoming telephone lines. Let the random variable X

ID: 3149955 • Letter: A

Question

An accounting office has six incoming telephone lines. Let the random variable X = the number of busy lines. The probability distribution function for X is given below.

X

0

1

2

3

4

5

6

F(X)

0.052

0.154

0.232

0.240

0.174

0.105

0.043

a) Find the expected number of busy lines when someone calls?

b) Find the cumulative distribution (cdf) for X?

c) During the first two weeks in April the firm experiences triple the number of calls it normally does. Find the expected number of busy lines during this time frame?

X

0

1

2

3

4

5

6

F(X)

0.052

0.154

0.232

0.240

0.174

0.105

0.043

Explanation / Answer

a.

f=   1  
fx =   2.817  
      
expected number of busy lines = Mean = fx / f =   2.817

c.

during first 2 weeks

f=   0.438
fx =   0.618
  
Mean = fx / f =   1.411

expected number of busy lines during this time frame = expected number of busy lines = Mean = fx / f =   1.411

Values ( X ) Frequency(f) fx ( X^2) f x^2 cumulative distribution 0 0.052 0 0 0 0 1 0.154 0.154 1 0.154 0.154 2 0.232 0.464 4 0.928 1.082 3 0.24 0.72 9 2.16 3.088 4 0.174 0.696 16 2.784 4.944 5 0.105 0.525 25 2.625 5.409 6 0.043 0.258 36 1.548 4.173
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