17. –/6 points BBUnderStat11 5.2.023. Ask Your Teacher My Notes Approximately 70

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17.–/6 pointsBBUnderStat11 5.2.023.

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My Notes

Approximately 70% of all marketing personnel are extroverts, whereas about 50% 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?

Question Part Points Submissions Used

Explanation / Answer

Binomial Distribution

Approximately 70% of all marketing personnel are extroverts, whereas about 50% of all computer programmers are introverts. (Round your answers to three decimal places)

Here, we have to find the P(X10)

We are given that n = 15 and p = 0.70

P(X10) = 1 – P(X<10)

P(X<10) = P(X9)

P(X9) = 0.278379

P(X10) = 1 – P(X<10) = 1 - P(X9) = 1 – 0.278379 = 0.721621

Required probability = 0.721621

What is the probability that 5 or more are extroverts?

n = 15 and p = 0.70

P(X5) = 1 – P(X<5) = 1 – P(X4)

P(X4) = 0.000672

P(X5) = 1 – P(X<5) = 1 – P(X4) = 1 – 0.000672 = 0.999328

Required probability = 0.999328

What is the probability that all are extroverts?

We are given n = 15 and p = 0.70

We have to find P(X=15)

P(X=15) = 0.004748

Required probability = 0.004748

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

We are given n = 4 and p = 0.50

We have to find P(X=0)

P(X=0) = 0.0625

Required probability = 0.0625

What is the probability that 2 or more are introverts?

We are given n = 4 and p = 0.50

We have to find P(X2)

P(X2) = 1 – P(X<2) = 1 – P(X1) = 1 – P(X=0) – P(X=1)

P(X=0) = 0.0625

P(X=1) = 0.2500

P(X2) = 1 – P(X<2) = 1 – P(X1) = 1 – 0.0625 – 0.2500 = 0.6875

Required probability = 0.6875

What is the probability that all are introverts?

We are given n = 4 and p = 0.50

We have to find P(X=4)

P(X=4) = 0.0625

Required probability = 0.0625

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