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%

In the bookA Guide to the Development and Use of the Myers-Briggs Type Indicatorsby Myers and McCaully, it was reported that approximately 45% of all university professors are extroverted. Suppose you have classes withthreedifferent professors.

(a) What is the probability that allthreeare extroverts? (Round your answer to three decimal places.)

(b) What is the probability that none of your professors is an extrovert? (Round your answer to three decimal places.)

(c) What is the probability that at least two of your professors are extroverts? (Round your answer to three decimal places.)

(d) In a group ofthreeprofessors selected at random, what is theexpected numberof extroverts? (Round your answer to two decimal places.)

_______ extroverts

What is thestandard deviationof the distribution? (Round your answer to two decimal places.)

______ extroverts

(e) Suppose you were assigned to write an article for the student newspaper and you were given a quota (by the editor) of interviewing at least three extroverted professors. How many professors selected at random would you need to interview to be at least89%sure of filling the quota?

______ professors

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