In the binomial probability distribution, let the number of trials be n = 8, and let the probability of success be p = 0.3499. Use a computer to determine the following.
(a) The probability of seven successes. (Use 4 decimal places.)
(b) The probability of eight successes. (Use 4 decimal places.)
(c) The probability of seven or eight successes. (Use 4 decimal places.)
In the book "A Guide to the Development and Use of the Myers-Briggs Type Indicators," it was reported that approximately 45% of all university professors are extroverted. Suppose you have completed classes with fourteen different professors.
(a) What is the probability that all fourteen are extroverts? (Use 5 decimal places.)
(b) What is the probability that none of your professors is an extrovert? (Use 5 decimal places.)
(c) What is the probability that at least two of your professors are extroverts? (Use 3 decimal places.)
(d) In a group of fourteen professors selected at random, what is the expected number of extroverts? What is the standard deviation of the distribution? (Use 2 decimal places.)
μ
σ
(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 least 90% sure of filling the quota?
n =
(a) A telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 6 to 18. What is the probability of a successful call? (Enter exact fraction or a decimal answer to a minimum of 3 places.)
(b) A sports announcer says that the odds a basketball player will make a free throw shot are 2 to 5. What is the probability the player will make the shot? (Enter exact fraction or a decimal answer to a minimum of 3 places.)