Mathematics and Statistical Sciences Department. Jackson State University. Fall
ID: 3310599 • Letter: M
Question
Mathematics and Statistical Sciences Department. Jackson State University. Fall 2017. Dr. Diatta, MATH 307 Exam 3 Date: 11/27/2017. Time 08: 00-08: 50 am. Name: J#: NB: No partial credits. No phone is allowed to be used as a calculator, and failing to comply will result in a grade of " F". Explain steps and show details. # 1, 25 pts 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 10 incoming calls. What is the probability that 1. At most 6 of the calls involve a fax message? 2. Exactly 4 of the calls involve a fax message? 3. At least 2 of the calls involve a fax message?
Explanation / Answer
Ans:
Binomial distribution with n=10,p=0.20
P(x=k)=10Ck*0.2k*(1-0.2)10-k
1)
P(at most 6)=P(x<=6)=10C0*0.20*0.810+10C1*0.21*0.89+..........+10C6*0.26*0.84
=0.1074+0.2684+0.3020+0.2013+0.0881+0.0264+0.0055
=0.9991
2)P(x=4)=10C4*0.24*0.86=0.0881
3)P(x>=2)=1-P(x<=1)=1-10C0*0.20*0.810-10C1*0.21*0.89
=1-0.1074-0.2684
=0.6242
x p(x) 0 0.1074 1 0.2684 2 0.3020 3 0.2013 4 0.0881 5 0.0264 6 0.0055 7 0.0008 8 0.0001 9 0.0000 10 0.0000