Name: ______

Quiz #2 – Chapter 3&4

Fall 2005

Math 63

Instructions: For each problem show all your work, including that work which will lead to the answer of a short answer type problem.

1. On an exam on probability, Sue had an answer of 13/8 for one problem. Explain

how she knew that the result was incorrect.

2. Using the following contingency table answer the following questions:

Cancer / Heart Disease / Other
Smoker / 135 / 310 / 205 / 650
Non-Smoker / 55 / 155 / 140 / 350
190 / 465 / 345 / 1000

a)  Find the probability that a randomly chosen person was a smoker.

b) Find the probability that a randomly chosen person died of heart disease or

was a smoker.

c) Find the probability that a randomly chosen person died of heart disease and was a smoker.

*d) Find the probability that a randomly chosen smoker died of heart disease.

3. A bag contains 6 red marbles, 3 blue marbles and 7 green marbles. Find the

following probabilities based upon this scenario.

a)  What is the probability that a randomly chosen marble is blue?

b) What is the probability of drawing 2 red marbles in a row if the first

marble is replaced before the second is drawn?

c) What is the probability of drawing 2 red marbles in a row if the marble

first marble is not replaced before the second is drawn?

4. Assume that one student in your class of 27 is randomly selected to win a prize.

Would it be “unusual” for you to be that student? Explain your answer using

probability and a specific rule of thumb for what “unusual” is consider to be.

5. List the sample space of possible outcomes if a coin and a hexagonal die are

tossed.

6. Find the odds against correctly guessing the answer to a multiple choice test with

4 possible answers. Give your answer based upon P(not correct)/P(correct).

Show your work.

7. For the following frequency table giving the recorded amount of time each

customer spent waiting in line during peak business hours one Monday, answer

the following question. Show all work.

Waiting Time in Min / # of Customers
0-3 / 14
4-7 / 9
8-11 / 11
12-15 / 6
16-19 / 7
20-23 / 3
24-27 / 2

a) What is the complement of waiting more than 3 minutes?

b) What is the probability of waiting more than 3 minutes?

c) What is the probability of waiting at least 12 minutes?

d) What is the probability of waiting 8 to 15 minutes?

e) What is the probability of waiting at least 12 minutes or 8 to 15 minutes?


8. The IRS auditor randomly selects 3 tax returns from 49 returns of which 9 contain

errors. What is the probability that the auditor selects none of those containing

errors? Are these independent events? Show your work.

9. A firm uses trend projection and seasonal factors to simulate sales for a given

time period. It assigns “0” if sales fall, “1” if sales are steady, “2” if sales rise

moderately and “3” if sales rise a lot. The simulator generates the following

output.

0 1 0 2 2 0 0 1 2 3 2 0 2 0 2 2 1 2 3 1 2 2 2 0 3 0 0 2 1 2 1

a) What is the estimated probability that sales will rise at least moderately?

Show all work.

10. Determine which, if any of the following represent a probability distribution

function. State the reason(s) why it is or is not a pdf. If it does represent a pdf,

then find the mean and standard deviation. Show all work.

11. A contractor is considering a sale that promises a profit of $38,000 with a

probability of 0.7 or a loss (due to bad weather, strikes, etc.) of $16,000 with a

probability of 0.3. What is the expected profit?


12. Does the following scenario result in a binomial distribution? In order to support

your answer, make a check list of the characteristics met to be a binomial

distribution.

Spinning a roulette wheel 6 times, keeping track of the occurrences of a

winning number “16”.

13. Assume a procedure yields a binomial distribution with a trial repeated 12 times.

Use the binomial probability formula (write out the formula using n, p & q as given

here, but you may use your calculator to find nCr) to find the probability of 5 successes,

given the probability of a success on a single trial is 0.25.

14. A company manufactures batteries in batches of 18 and there is a 3% rate of

defects. Find the mean and standard deviation of the number on defects per batch.

15. For a randomly chosen sample of 18, what are the highest and lowest number of

defective batteries that will “usually” be found?

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