Reference no: EM132436402

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 5 different professors.

(a) What is the probability that all five 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 five professors selected at random, what is the expected number of extroverts? What is the standard deviation of the distribution?

(e) Suppose you were assigned to 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 least 84% sure of filling the quota?

a) What is the probability that all five are extroverts?

Recall that the binomial distribution with parameters n, p, and r gives the probability distribution of the number of r successes in a sequence of n trials, each of which yields success with probability p.

For this question, "success" can be defined as a professor being an extrovert. We are given that 45% of all university professors are extroverted. Therefore, each professor has a 45% chance of being extroverted. So, p = _______.

Here we have five different professors; each one could be an extrovert or not. So, n = _____.

To find the probability that all five professors are extroverts, we want five "successes." So, r = ____________