1. 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?
2. 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 has been pregnant at least once before age 18 will be exactly three.
3. 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.
4. 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 on paper and A on exam .25
A on paper only .15
A on exam only .20
A on neither .40
a. What is the probability of getting an A on the exam?
b. What is the probability of getting an A in the course?
The solution comprises of detailed step-by-step calculations of the given problems on probability.