Insurance: auto the mountain states office of state farm insurance company reports that approximately 85% of all automobile damage liability claims are made by people under 25 years of age. a random sample of five automobile insurance liability claims is under study. (a) make a histogram showing the probability that r = 0 to 5 claims are made by people under 25 years of age. (b) find the mean and standard deviation of this probability distribution. for samples of size 5, what is the expected number of claims made by people under 25 years of age? focus problem: personality types we now have the tools to solve the chapter focus problem. 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 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? (e) quota problem 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 least 90% sure of filling the quota?