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Topic: Test 4 (Chapter 4 BPS)
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Al Coons

Posts: 898
Registered: 12/4/04
Test 4 (Chapter 4 BPS)
Posted: Dec 14, 1996 11:24 AM
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In following the Bohan's for Workshop Statistics syllabus we covered Chapter
4 of BPS. Here is a test. All feedback & suggestions appreciated. Since I
have already borrowed some parts of this from many of you the rest of you
should feel free to borrow what is here without asking. We are now moving
into Topic 16 of Rossman/Workshop Statistics.

12/12/96 AP Statistics - Test 4 - BPS 4 + ABS Labs Mr. Coons

1a. True/False? Observations which are independent always have the same
probability of success. Explain your answer.

b. In addition to the two properties mentioned above, what are the other
requirements for a Binomial Setting?

c. Assume the probability for having a boy baby is 51%. Use binomial
probability calculations to find the probability of having exactly 3 boys
after 12 births? Show some supporting work.

2. Upon overhearing two AP Statistics students mention that they have been
making predictions while studying random phenomenon, a skeptic exclaims:
"Impossible. Another example of the inappropriate use of Statistics!
Randomness implies something cannot be predicted." Soothe the skeptic's
fears.

3. A class of four students represents our population. The students report
the following amount of money in their wallets: $10, $12, $14, & $16.

a) Create by hand a rough histogram of the population data.

b) Define Sampling Distribution.

c) Create by hand a rough histogram of the sampling distribution of the mean
of the money in their wallets for sample size 2. Show enough work to
demonstrate where the values came from.

d) What part of the hypothesis of the CLT for Sample Means is not fulfilled
by this problem?

e) Explain how, in very broad terms, parts a-c demonstrate the conclusions
CLT For Sample Means brings to statistics.

4. The probability that a three-year-old battery still works is 0.8. A
cassette recorder requires four working batteries to operate. The state of
batteries can be regarded as independent, and four three-year-old batteries
are selected for the cassette recorder. What is the probability that the
cassette recorder operates?

a. 0.9984 b. 0.8000 c. 0.4096 d. 0.5904

5. The distribution of actual weights of 8 oz. chocolate bars produced by a
certain machine is normal with mean 8.1 ounces and standard deviation 0.1
ounces. A sample of 5 of these chocolate bars is selected. There is only a 5%
chance that the average weight of the sample of 5 of the chocolate bars will
be below what weight? Show your work.

6. The IRS estimates that 7% of all taxpayers filling out long tax forms
make mistakes. Suppose that a random sample of 10,000 forms are selected.
What is the approximate probability that fewer than 690 forms contain
mistakes? Show detailed work, labeling with approximate symbols as often as
possible.

7. The sampling distribution for the means for sample size 9 of ages of the
10,111 men in a tribe in Africa seems very close to N(42, 4). Approximately
what is the standard deviation of the population?

8. a. True/False. A x-bar-control chart is created by taking repeated SRS
of a fixed size. Briefly support your answer.

b. A manufacturing process produces bags of cookies. The distribution of
weights of these bags should have a mean of 15.0 oz and a standard deviation
0.4 oz. In order to monitor the process, 4 bags are selected periodically and
their average weight is determined. These values of x-bar are plotted on
an x-bar control chart.

Suppose, by mistake, the value of single bags are now recorded on the control
chart rather than the value of . What proportion of times will one observe
these points falling outside the control limits? Show detailed work.

9. True/False: The Law of Large Numbers suggests that as you flip a fair
coin more and more times the actual number of heads gets closer and closer to
.5n where n is the number of flips. Create an example to support your answer.











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