A particular telephone number is used to receive both voice calls and fax messag
ID: 3244444 • Letter: A
Question
A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 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 question.Explanation / Answer
Answer:
n=20, p=0.20. Binomial distribution used.
a). P( x5) = 0.804
b).P( x=5) = 0.175
c). P(x 5) = 0.370
d). P( x >5) = 0.196
Binomial Probabilities Table
X
P(X)
0
0.01153
1
0.05765
2
0.13691
3
0.20536
4
0.21820
5
0.17456
6
0.10910
7
0.05455
8
0.02216
9
0.00739
10
0.00203
11
0.00046
12
0.00009
13
0.00001
14
0.00000
15
0.00000
16
0.00000
17
0.00000
18
0.00000
19
0.00000
20
0.0000
Binomial Probabilities Table
X
P(X)
0
0.01153
1
0.05765
2
0.13691
3
0.20536
4
0.21820
5
0.17456
6
0.10910
7
0.05455
8
0.02216
9
0.00739
10
0.00203
11
0.00046
12
0.00009
13
0.00001
14
0.00000
15
0.00000
16
0.00000
17
0.00000
18
0.00000
19
0.00000
20
0.0000