Decision Theosy practice problem I. The weight of a one cubic yard bag of landsc

Question

Decision Theosy practice problem

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 1 pound.

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

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

II. According to the Spring 2009 issue of the periodical Zero Population Growth, the U.S. leads the fully industrialized world in teen pregnancy rates, with 25% of U.S. females getting pregnant at least once before the age of 20. Suppose that 10 U.S. females are selected at random. Find the probability that the number who have been pregnant at least once before age 20 will be exactly three. (hint: use the binomial probability distribution)

III. It is estimated that 20% 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.

            (hint: draw the tree diagram for this problem, similar to the one we did in class last week.

IV.     A company has fixed cost of $100,000, variable cost per unit of $10, and sells its product at $14 each.

                        a. What quantity must the firm sell in order to break even?

                        b.   What quantity must the firm sell in order to make a profit of $50,000?

V. If P(A) = 0.40, P(B) = 0.80, and P(A and B) = 0.30

Determine whether A and B are independent. Show your calculation.

Determine   P(A or B) =

Explanation / Answer

Decision Theosy practice problem I. The weight of a one cubic yard bag of landsc

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