Approximately 70% of all marketing personnel are extroverts, whereas about 65% o

Question

Approximately 70% of all marketing personnel are extroverts, whereas about 65% of all computer programmers are introverts. (Round your answers to three decimal places.)

(a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?


What is the probability that 5 or more are extroverts?


What is the probability that all are extroverts?


(b) In a group of 4 computer programmers, what is the probability that none are introverts?


What is the probability that 2 or more are introverts?


What is the probability that all are introverts?

Explanation / Answer

ans=

Binomial distribution is to be used

P(x) = nCx*p^x*q^(n-x)

a) p=65% = 0.65

q = 1-p = 1-0.65 = 0.35

n = 15

i) Required probability = P(x >/= 10)

= P(x=10) + P(x=11) + .....+ P(x=15)

ii) Required probability = P(x>/= 5)

= 1 - [P(x=0)+P(x=1)+... +P(x=4)]

iii) Required probability = P(x=15)

= 15C15*0.65^15*0.35^0

= 0.0016

b) p=70% = 0.7

q = 1-0.7 = 0.3

n = 5

i) Required probability = P(x=0) = 5C0*0.7^0*0.3^5

= 0.00243

ii) Required probability = P(x >/= 3)

= P(x=3)+P(x=4)+P(x=5)

iii) Required probability = P(x=5) = 5C5*0.7^5*0.3^0

= 0.16807

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