Decision Theory First Quiz    Answer all of the following Roman numeral questions (I, II, III, IV). Equal credit.     I. The weight of a...

Decision Theory

First Quiz 

Answer all of the following Roman numeral questions (I, II, III, IV). Equal credit.

I. The weight of a one cubic yard bag of landscape mulch is normally distributed with a mean of 40 pounds and a standard deviation of 2 pounds.

a.              What is the probability that a bag will weigh less than 40 pounds?

b.              What is the probability that a bag will weigh between 38 and 40 pounds?

II. According to the Spring 2014 issue of the periodical Zero Population Growth, the U.S. leads the fully industrialized world in teen pregnancy rates, with 20% of U.S. females getting pregnant at least once before the age of 18.  Suppose that 15 U.S. females are selected at random.  Find the probability that the number who have been pregnant at least once before age 18 will be exactly three.

III. It is estimated that 10% of the athletes competing in a large tournament are users of an illegal drug to enhance performance.  The test for this drug is 95% accurate.  Determine the probability that an athlete who tests positive is actually a user.

IV. There are two more assignments in a class before its end, and if you get an A on at least one of them, you will get an A for the semester. Your subjective assessment of your performance is

  a. What is the probability of getting an A on the exam? 

  b. What is the probability of getting an A in the course?