We now have the tools to solve the Chapter Focus Problem. Inthe book A Guide to

Question

We now have the tools to solve the Chapter Focus Problem. Inthe book A Guide to the Development and Use of the Myers-BriggsType Indicators by Myers and McCaully, it was reported thatapproximately 45% of all university professors are extoverted.Suppose you have classes with six different professors. a. What is the probability that all six are extroverted? b. What is the probability that none of your professors areextroverted? c. What is the probability that at least two of yourprofessors are extroverted? d. In a group of six professors selected at random, what isthe expected number of extroverts? What is the standard deviationof the distribution? We now have the tools to solve the Chapter Focus Problem. Inthe book A Guide to the Development and Use of the Myers-BriggsType Indicators by Myers and McCaully, it was reported thatapproximately 45% of all university professors are extoverted.Suppose you have classes with six different professors. a. What is the probability that all six are extroverted? b. What is the probability that none of your professors areextroverted? c. What is the probability that at least two of yourprofessors are extroverted? d. In a group of six professors selected at random, what isthe expected number of extroverts? What is the standard deviationof the distribution?

Explanation / Answer

This is a binomial distribution question. Let X be the number of extroverted X~(n = 6, p = 0.45) (a) P(X = 6) =6C6(0.45)6(0.55)0 =0.0083 (b) P(X = 0) =6C0(0.45)0(0.55)6 =0.0277 (c) P(At least 2) = 1 - P(X = 0) - P(X = 1) = 1 - 0.0277 -6C1(0.45)1(0.55)5 =0.8364 (d) Expected number of extroverts = 6 x 0.45 = 2.7 (3extroverts)      Standard deviation = (npq) =(6 x 0.45 x 0.55) = 1.22 Hope this helps!

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