Part I : Simple Counting Place your answer in the space provided.

___________ 1. ) If there are three boys and four girls at a basketball game

together , how many ways can all three boys sit together ?

___________ 2. ) How many different ways can we be dealt 5 cards of the same

suit from a standard 52 card deck ?

Part II : Multiple Choice Place the correct letter beside each question.

__________ 3. ) For a continuous distribution what is the probability that x takes on a specified value exactly ( P ( X = x) ) ?

A. ) 0

B. ) need the normal table first

C. ) 1

D. ) need to know the z - score first

_________ 4. ) Which of the following is NOT a valid statement of the probability of an event, A ?

A. ) P( A ) = 0 . 0

B. ) P ( A ) = 1 . 0

C. ) P ( A ) = 0 . 758473535

D. ) P ( A ) = - 0 . 67

_________ 5. ) When dealing with a general normal distribution what distribution do we usually change it to so we can find the probability ?

A. ) the standard normal distribution

B. ) the uniform distribution

C. ) a generic discrete distribution

D. ) Any Distribution will work

_________ 6. ) A radio station claims that the amount of advertising per hour of broadcast time is normally distributed with an average of 3 minutes and a standard deviation equal to 2.1 minutes. You listen to the radio station for one hour, at a randomly selected time during the day, and carefully observe that the amount of advertising is equal to 7 minutes. Calculate the z - score for this amount of advertising time.

A. ) z = 1.63

B. ) z = 1.90

C. ) z = 4.00

D. ) z = - 1.90

________ 7. ) If a fair coin is flipped twice with the outcome of each flip independent of each other, then the probability that at least one of the two flips results in a head is

A. )

B. )

C. )

D. ) 1

________ 8. ) Only 20 % of the applicants for new positions at a large software company are female. Assuming that two positions will be filled independently of each other, what is the probability that both positions are filled by males ?

A. ) . 64

B. ) . 04

C. ) . 96

D. ) . 8

________ 9. ) A large family is going shopping for a new van. The probability that the family will purchase a Ford van is . 33 . The probability of purchasing a Chevy van is .25. The probability of purchasing a Dodge is .20 , and the probability of purchasing a Toyota is .22 . What is the probability the family will end up purchasing a Ford or Chevy or Dodge van ?

A. ) .0165

B. ) .22

C. ) .78

D. ) .75

Part IV : Computational Problems

For Problems 10 - 11 use the following information :

The number of days of sick-leave used in a year by state employees for the state of Tennessee has a normal distribution with a mean of 9 days and a standard deviation of 2 days.

10. ) What is the probability that a state employee from Tennessee will use more than 13 days of sick leave in a year ?

11. ) About 16.11 % of the state employees use fewer than how many sick leave days in a year ?

A college math professor has surveyed her records and found the following frequency distribution of the grades she has assigned to the 1187 students who have taken her calculus classes.

GRADE A B C D F

Frequency 125 352 461 187 62

12. ) What is the probability that a randomly selected student received an A in calculus from this professor ?

13. ) What is the probability that two independently selected students both received an A in calculus from this professor ?

14. ) Janice wants to become a police officer. She must pass a

physical exam and then a written exam. Records show the probability of passing the physical exam is 0.85 and that once the physical is passed the probability of passing the written exam is 0.60. What is the probability that Janice passes both exams ?

15. ) Given the following probability distribution find the mean and

variance for the distribution : for x=1,2,3 or 4 .

16. ) In California, 30% of the people have a certain blood type.

What is the probability that exactly 5 out of a randomly selected group of 14 Californians will have that blood type ?

It is believed that 58% of married couples with children agree on methods of disciplining their children. If 200 couples are surveyed answer the following two questions :

17. ) Find the probability that exactly 110 couples agree.

18. ) Find the probability that more than 100 couples agree.

19. ) Find .

20. ) The baggage weights for passengers using a particular airline

are normally distributed with a mean of 20 lb and standard deviation of 4. Find the probability that 100 passengers will have an average baggage weight of more than 21.25 lbs.