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Statistics- Chapter 9 Practice B
Name: _____________________
Date: __________ Hour: _______
I
II
III
IV
V
Objective I
1.
In a study of the effects of acid rain, a simple random sample of 100 trees from a particular forest is
examined. Forty percent of these show some signs of damage.
a.
What is the mean of the sampling distribution of p̂ , the proportion of trees in samples of 100 that sho
signs of acid rain damage?
b. What is the standard deviation of p̂ ?
c.
What is the probability that more than 25 trees in the sample shows signs of damage? (Sketch
required.)
2. In a large population of adults, IQ is normally distributed with a mean of 112 with a standard deviation of
20.
a.
What is the probability that a randomly person from the described population has an IQ greater than
130? (Sketch required.)
b. Describe the shape of the sampling distribution of the mean x of a sample of 100 randomly selected
people from the described population.
c.
What are the mean and standard deviation for the IQ of an SRS of 100 people from the population?
d. What is the probability that the average IQ of an SRS of 100 people from the described population is
greater than 130?
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Statistics- Chapter 9 Practice B
Objective II
3. Explain why you can use the formula for the standard deviation of p̂ in the setting in number 1.
4. Explain why you can use the normal approximation for the distribution of p̂ to calculate #2d.
5. Would your answers to #2(a-d) be affected if the distribution of IQ were distinctly nonnormal? Explain.
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Statistics- Chapter 9 Practice B
Objective III6. A simple random sample of 1000 Americans found that 61% were satisfied with the service provided by the
dealer from which they bought their car. A simple random sample of 1000 Canadians found that 58% were
satisfied with the service provided by the dealer from which they bought their car. Describe the sampling
variability associated with American Service compared to the sampling variability associated with Canadian
Service. Explain
7. Suppose we are planning on taking an SRS from a population. If we multiply the sample size by 1/3 , then
x
will be multiplied by___________
8. Going back to #1 in which 40% of the trees showed acid rain damage, how large a sample would be needed to
guarantee that the standard deviation of p̂ is no more than 0.05?
9. In a large population of adults, IQ is normally distributed with a mean of 112 with a standard deviation of
20. What is the IQ, X such that there is a probability of 0.20 that the mean X for the 100 people sampled
is above this level?
Objective IV
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Statistics- Chapter 9 Practice B
A survey conducted by the VanderLeest Polling Organization discovered that 18% of all Americans knowingly
cheat on their taxes. Suppose that a number of randomly selected Americans are polled.
10. Find the probability that 15 of the 100 polled cheat on their taxes. Show the binomial formula.
11. Find the probability that between 30 and 50 of the 100 polled cheat on their taxes.
12. If someone were conducting the poll, what is the probability that they would have to contact 10 Americans
before someone answered that they cheat on their taxes.
13. What is the probability that they have to contact more that 8 Americans before someone answers that they
cheat on their taxes?
14. Again, assume that 100 Americans are polled. Let X= the number of people that answer that they knowingly
cheat on their taxes. What is the mean and standard deviation of X. Show all formulas uses.
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