Question

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

Answer 1

Probability of a professor being extrovert=0.45
Let X be the no. of professors who are extrovert then X~Binomial(3,0.45) with

a)Probability of all three being extrovert:

b)Probability of none being extrovert:

c)Probability of atleast 2 being extrovert:

d)For a binomial distribution expectation is given as:n*p
where n=3 and p=0.45

E(X)=3*0.45=1.35
e) Standard deviation is given as: