My Notes Ask Your Teacher Round your answers to 20 -14 points devoresta:93.e.050

Question

My Notes Ask Your Teacher Round your answers to 20 -14 points devoresta:93.e.050.nva 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 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 S of the calls involve a fax message? You may need to use the appropriate table in the Appendix of Tables to answer this question Need Help?Tak to a Tutor

Explanation / Answer

X ~ Binomial (n,p)

Where,

n = 20, p = 0.20

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

a)

P( X <= 5) = P( X =0) + P( X =1) + P( X =2) + P( X =3) + P( X =4) + P( X =5)

= 20C0 0.200 0.8020 +20C1 0.201 0.8019 +20C2 0.202 0.8018 +20C3 0.203 0.8017 +20C4 0.204 0.8016

+ 20C5 0.205 0.8015

= 0.8042

b)

P( X = 5) = 20C5 0.205 0.8015

= 0.1746

c)

P( X >= 5) = 1 - P( X <= 4)

= 1 - {  P( X =0) + P( X =1) + P( X =2) + P( X =3) + P( X =4) }

= 1 - { 20C0 0.200 0.8020 +20C1 0.201 0.8019 +20C2 0.202 0.8018 +20C3 0.203 0.8017 +20C4 0.204 0.8016 }

= 0.3704

d)

P( X > 5) = 1 - P( X <= 5)

= 1 - 0.8042 (Probability calculated in part a)

= 0.1958

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