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.