Mathematics and Statistical Scienoes Department Jackson State Unlversity Fall 20
ID: 3310595 • Letter: M
Question
Mathematics and Statistical Scienoes Department Jackson State Unlversity Fall 2017 Dr. Diatta, MATH 307 Exam3 Dater 11/27/2017, Tioe 08: 00-08 30 am NB: No partial credits. No phone is allowed to be used as a calculator and fniling to comply will ressslt in a grade of "F". Explain steps and sbow details 1, 25 pts A particular telephone number "and to reoive both voice calls nad fax rne sages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 10 incoming calls. What is the probability that I. At most 6 of the calls involve a fax message? ax messages 2. Exactly 4 of the calls involve a fax message? 3. At least 2 of the calls involve a fax messnge? 4. More than 3 of the calls involve a fax message?Explanation / Answer
p = 0.2
n = 10
This is binomial distribution
P(X = x) = 10Cx * 0.2x * (1 - 0.2)10-x
a) P(X < 6) = 1 - (P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10))
= 1 - (10C7 * 0.27 * 0.83 + 10C8 * 0.28 * 0.82 + 10C9 * 0.29 * 0.81 + 10C10 * 0.210 * 0.80 )
= 1 - 0.0009
= 0.9991
b) P(X = 4) = 10C4 * 0.24 * 0.86 = 0.0881
c) P(X > 2) = 1 - (P(X = 0) + P(X = 1))
= 1 - (10C0 * 0.22 * 0.88 + 10C1 * 0.21 * 0.89 )
= 1 - 0.3758
= 0.6242
d) P(X > 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))
= 1 - (10C0 * 0.22 * 0.88 + 10C1 * 0.21 * 0.89 + 10C2 * 0.22 * 0.88 + 10C3 * 0.23 * 0.87 )
= 1 - 0.8791
= 0.1209