A particular telephone number is used to receive both voice calls and fax messag
ID: 3244481 • Letter: A
Question
A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 5 of the calls involve a fax message? (b) What is the probability that exactly 5 of the calls involve a fax message? (c) What is the probability that at least 5 of the calls involve a fax message? (d) What is the probability that more than 5 of the calls involve a fax message? You may need to use the appropriate table in the Appendix of Tables to answer this questionExplanation / Answer
This is the case Binomial Distribution.
n = 25
p = 0.25
p (x) = C(n,x) * p^x * (1-p)^(n-x)
x
Formula
P (x)
0
C(25,0) * 0.25^0 * 0.75^25
0.0008
1
C(25,1) * 0.25^1 * 0.75^24
0.0063
2
C(25,2) * 0.25^2 * 0.75^23
0.0251
3
C(25,3) * 0.25^3 * 0.75^22
0.0641
4
C(25,4) * 0.25^4 * 0.75^21
0.1175
5
C(25,5) * 0.25^5 * 0.75^20
0.1645
Question a)
P ( x <= 5 ) = P ( x = 0 ) + P ( x = 1 ) + P ( x = 2 ) + P ( x = 3 ) + P ( x = 4 ) + P ( x = 5 )
= 0.0008 + 0.0063 + 0.0251 + 0.0641 + 0.1175 + 0.1645
= 0.378
Answer: 0.378
Question b)
P (x = 5) = 0.165
Answer: 0.165
Question c)
P ( x >= 5 ) = 1 – P ( x < 5 )
= 1 – [ P ( x = 0 ) + P ( x = 1 ) + P ( x = 2 ) + P ( x = 3 ) + P ( x = 4 ) ]
= 1 – [= P ( x = 0 ) + P ( x = 1 ) + P ( x = 2 ) + P ( x = 3 ) + P ( x = 4 )]
= 1 – 0.2137
= 0.786
Answer: 0.786
Question d)
P ( x > 5 )
P ( x > 5 ) = 1- P ( x <= 5 )
= 1 – 0.378
= 0.622
Answer: 0.622
x
Formula
P (x)
0
C(25,0) * 0.25^0 * 0.75^25
0.0008
1
C(25,1) * 0.25^1 * 0.75^24
0.0063
2
C(25,2) * 0.25^2 * 0.75^23
0.0251
3
C(25,3) * 0.25^3 * 0.75^22
0.0641
4
C(25,4) * 0.25^4 * 0.75^21
0.1175
5
C(25,5) * 0.25^5 * 0.75^20
0.1645
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