FOR INSTRUCTORS USE

1.

a......../7

b....../6

c......./6

d......./6

SUBTOTAL........../25

2.	a......../5	b....../5	c......./5	d......./5
	e......../5	f......./5
	SUBTOTAL........../30

3.	a......../5	b....../5	c......../5	d......../5
	e......../5	SUBTOTAL........../25

4.	a......../8	b....../6	c......../6
	SUBTOTAL........../20

TOTAL

........../100

1. An automobile dealer conducted a test to determine if the time needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, each analyzer is used for the three types of cars.

a. Is this an experiment? Why or why not?

b. What are the experimental units?

c. What are the factor(s) (explanatory variable(s)). What are the levels of each factor? Define the treatments.

d. What is the response variable?

2. Psychologists believe that there is a relationship between aggressiveness and order of birth. To test this belief, a psychologist collected data from elementary school children and she provided the following assignment of probabilities:

			ORDER OF BIRTH
		Firstborn	Secondborn	Other
	Aggressive	.06	.10	.08
AGGRESSIVENESS
	Unaggressive	.12	.33	.31

a. What is the probability that a randomly selected student is aggressive?

b. What is the probability that a randomly selected student is aggressive and firstborn?

c. What is the probability that a randomly selected student is secondborn given that the student is aggressive?

d. What is the probability that a randomly selected student is unaggressive given that the student is secondborn?

e. What is the probability that a randomly selected student is aggressive or firstborn?

f. Are the events "student being aggressive" and "student being secondborn" independent? Are they disjoint? Please justify your answer.

3. A parole officer has just interviewed each inmate in the state's correctional facilities to determine the number of previous convictions, X, each had prior to the one for which he or she is now serving time. The following results were obtained:

Number of Previous Convictions	0	1	2	3	4
Probability	0.03	0.62	0.19	0.09	0.07

a. Is this a legitimate probability distribution? Please justify your answer.

b. Find the mean

c. Find the standard deviation

d. What is the probability that a randomly selected inmate will have 3 or more previous convictions?

What is the probability that a randomly selected inmate will have 3 previous convictions given that he or she has at least 3 previous convictions?

e. Assume that the number of previous convictions for an inmate is independent of the number of previous convictions of other inmates. Suppose that three inmates are selected. What is the probability that each of the three inmates selected will have 2 previous convictions?

4. A large soap company is planning to introduce a new dish-washing detergent into the market. In the past, 35% of the products introduced by the company have been successful and 65% of the products have not been successful. Before the product is actually marketed, market research is conducted and a report (favorable or unfavorable) must be prepared. In the past, 75% of the successful products received favorable reports and 25% of the unsuccessful products also received favorable reports.

a. Draw a tree diagram that summarizes this information.

b. What is the probability that a randomly selected product will receive a favorable report?

c. If the dish-washing detergent receives a favorable marketing report, what is the probability that it will indeed be successful?