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 4.173Related Questions
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