In the bookManual: A Guide to the Development and Use of the Myers-Brigg Type Indicator, by Myers and McCaulley, it was reported that based on a very large sample (2282 professors), approximately 45% of all university professors were extroverted. Suppose you have classes with six different professors; a) What is the probability thta 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?