10. . In the book A Guide to the Development and Use of | the Myers-Briggs Type

Question

10. . In the book A Guide to the Development and Use of | the Myers-Briggs Type Indicators by Myers and McCaully, it was report that approximately 45% of all university professors are extroverted. Suppose you have classes with six different professors. (a) What is the probability that all six are extroverts? (b) What is the probability that none of your professors is an extrovert? (c) What is the probability that at least two of your professors are extroverts? (d) In a group of six professors selected at random, what is the expected number of extroverts? What is the standard deviation of the distribution'?

Explanation / Answer

1)this is binomial distribution; p=0.45 ; n=6

a) P(X=6) =(0.45)6 =0.0083

b)P(X=0) =(1-0.45)6 =0.0277

c)P(X>=2) =1-P(X<=1) =1-(P(X=0)+P(X=1) ) =1-(.0277+.1359)=0.8364

d)

expected number =np =6*0.45=2.7

std deviation =(np(1-p))1/2 =1.2186

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