Approximately 65% of all marketing personnel are extroverts, whereas about 55% o
ID: 3245699 • Letter: A
Question
Approximately 65% of all marketing personnel are extroverts, whereas about 55% of all computer programmers are introverts. (Round your answers to three decimal places.) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts? 0.721 What is the probability that 5 or more are extroverts? ______ What is the probability that all are extroverts? ______ In a group of 5 computer programmers, what is the probability that none are introverts? ______ What is the probability that 3 or more are introverts? ______ What is the probability that all are introverts? ______Explanation / Answer
65% of all marketing personals are extroverts, probability of extroverts = 0.65
55% of all computer programmers are introverts, probability of introverts = 0.55
a) sample size n = 15
Probability that 10 or more are extroverts
P(x 10) = 1- P(x < 10)
= 1- [P(x=9)+P(x=8)+P(x=7)+P(x=6)+P(x=5)+ P(x=4)+P(x=3)+P(x=2)+P(x=1)]
=1-BINOMDIST(9,15,0.65,TRUE) [using MS-excel]
=1-0.436
=0.564
Probability that 5 or more are extroverts
P(x5) = 1-P(x<5)
=1 –[P(x=4)+P(x=3)+P(x=2)+P(x=1)]
=1- BINOMDIST(4,15,0.65,TRUE) [using MS-excel]
= 1-0.003
=0.997
Probability that all are extroverts
P(x=15) =BINOMDIST(15,15,0.65,0) [using MS-excel]
= 0.00156
=0.006
b) sample size n=5
Probability of none of is introverts
P(x=0) =BINOMDIST(0,5,0.55,0) [using MS-excel]
=0.018
Probability of 3 or more are introverts
P(x 3) = 1-P(x<3)
= 1- [P(x=2)+P(x=1)]
=1-BINOMDIST(2,5,0.55,TRUE) [using MS-excel]
=1-0.407
=0.593
Probability of all are introverts
P(x=5) =BINOMDIST(5,5,0.55,0) [using MS-excel]
=0.050
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