Part I :  Counting Probabilities  LEAVE ANSWERS AS A FRACTION

___________  1. )       Find the probability of obtaining a pair first and then 5 other

cards that do not match the pair if you are dealt 7 cards from a standard 52 card deck?

___________  2. )       In the New York State Lottery, a person wins first prize by

selecting the correct 6-number combination ( order does not matter ) when 6 different numbers from 1 through 51 are drawn.  Find the probability that a person wins the lottery if they select 6 numbers ?

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

( 3 points each )

__________  3. )         For the standard normal distribution what is ( P ( Z = 0) ) ?

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.  )         Only 20 % of the applicants for new positions at a large

software company are female.  Assuming that three positions will be filled independently of each other, what is the probability that all the positions are filled by males ?

A.     )     0 .  640

B.     )     0 .  512

C.     )     0 .  040

D.    )     0 .  008

Part III :  Computational Problems

For Problems 6 - 7 ,  use the following information :

The Binary Computer Company manufactures computer chips used in DVD players.  Those chips are made with a 27% yield, meaning that 27% of them are good and the others are defective.

___________  6. )       If one chip is randomly selected, find the probability that it is not good.

___________  7. )       If two chips are randomly selected, find the probability that they are both good.

___________  8. )       The New England Life Insurance Company issues one-year policies to 12 men who are all 27 years of age.  Based on the data from the Department of Health and Human Services, each of these men has a 99.82 % chance of living through the year.  What is the probability that they all survive this year ?

___________  9. )       A batch of light switches contains 44 that are good and 4 that are defective.  Four different switches are selected without replacement from the batch, find the probability that they are all good.

For Problems 10 - 14,  use the following information :

The television show ER has a 34 share, meaning that while it is being broadcast, 34 % of the TV sets in use are tuned to ER ( based on data from Nielson Media Research ).  Assume that during a broadcast of ER, 20 TV sets are randomly selected from those that are in use.

___________  10. )     Find the mean number of TV sets tuned to ER.       ( 3 points )

___________  11. )      Find the variance of TV sets tuned to ER.               ( 3 points )

___________  12. )     Find the standard deviation of TV sets tuned to ER. ( 3 points )

___________  13. )     Find the probability that exactly 5 TV sets are tuned to ER.

___________  14. )     Find the probability that more than 7 TV sets are tuned to ER.

For Problems 15 - 16,  use the following data obtained from a test of Nicorette, a chewing gum designed to help people stop smoking.  The following table is based on data from Merrell Dow Pharmaceuticals, Inc. :

Nicorette                  Placebo

Mouth or throat soreness                                43                           35

No mouth or throat soreness             109                         118

___________  15. )     If one subject is selected at random, find the probability that he or she experienced mouth or throat soreness or used a placebo.

___________  16. )     If one subject is selected at random, find the probability that he or she experienced mouth or throat soreness, given that the selected person used a placebo.

__________    17. )     Find ( 4 points )

__________    18. )     Find                   ( 4 points )

For Problems 19 - 23,  use the following information :

The annual precipitation amounts for Iowa appear to be normally distributed with a mean of 32.473 in. and a standard deviation of 5.601 in.

( Based on data from the U.S. Department of Agriculture ).

_________      19. )     If 1 year is randomly selected, find the probability that the

annual precipitation is less than 29.000 in.

_________      20. )     If 1 year is randomly selected, find the probability that the

annual precipitation is less than 38.250 in.

21. )     Describe the distribution of , for samples of size 10.      ( 4 points )

_________      22. )     If a decade of 10 years is randomly selected, find the

probability that the annual precipitation amounts have a mean less than 29.000 in.

_________      23. )     Assume that cans of Pepsi are filled so that the actual amounts

have a mean of 12.00 oz and a standard deviation of 0.09 oz.  Find the probability that a sample of size 36 cans will have a mean amount of at least 12.29 oz. or more.