** Part I : Counting
Probabilities LEAVE ANSWERS AS A
FRACTION**

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___________ 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?

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**___________ 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 ?**

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

**( 3 points
each )**

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

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**A. ****) 0 **

**B. ****) need the normal table first**

**C. ****) 1 **

**D. ****) need to know the z - score
first**

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

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**A. ) P( A ) = 0 . 0**

**B. ) _{}P ( A ) = 1 . 0**

**C. ) P ( A ) =
- 0 . 758473535**

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

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**_________ 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 ?**

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**A. ****) 0 . 640**

**B. ****) 0 . 512**

**C. ****) 0 . 040**

**D. ****) 0 . 008**

**Part III
: Computational Problems **

**For Problems 6
- 7 , use the following
information :**

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**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.**

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

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

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___________ 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 ?

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___________ 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.

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**For Problems 10
- 14, use the following
information :**

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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.

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

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

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

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

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

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**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. :**

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** Nicorette Placebo**

** Mouth or throat soreness 43 35**

** No mouth or throat soreness 109 118**

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

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**___________ 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.**

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**__________ 17. ) Find
_{} ( 4 points )**

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**__________ 18. ) Find
_{} ( 4
points )**

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**For Problems 19
- 23, use the following
information :**

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**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 ).**

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

**annual precipitation is less than 29.000 in. **

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

**annual precipitation is less than 38.250 in. **

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**21. ) Describe the distribution of _{}, for samples of size 10. (
4 points )**

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**_________ 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. **

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**_________ 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.**