Download Chapter 7 REVIEW

Preparing for Your Chapter 7 Test
AP Statistics
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Name: ___________________________
Date: ____________________________
How to identify a parameter and a statistic from the context of the situation.
How to identify high/low bias and variability.
The exact definition of the important terms in the chapter such as: Sampling Distribution of a Statistic, Unbiased
Estimator, Variability of a Statistic, etc.
That the size of the sample is what impacts the spread (sampling variability) of the distribution.
How to find the mean of a sampling distribution (as long you have a SRS the mean of the sampling distribution
should equal that of the population) - Know the proper notation.
How to calculate the standard deviation of a sample mean and sample proportion (know the formulas and the
proper notation)
How to determine if a sampling distribution for proportions or means is approximately Normal
(np > 10 and
n(1-p) > 10 OR CLT)
The significance and use for the central limit theorem.
o If the population is normally distributed, then the sampling distribution will also be normal regardless of
the sample size.
o If the population is NOT normally distributed, then the sampling distribution becomes more and more
normal as the sample size increases. The larger the sample size, the more normally distributed we can
assume the data to be.
How to determine if you can use the standard deviation formula for sampling proportions and means (check the
10% condition/independent condition)
How to calculate probabilities based on the normal approximations using either Table A or the calculator
commands (normalcdf).
How to describe a sampling distribution. Address the following: shape, center, and spread. For example, “The
distribution is normal with a mean of ____ and a standard deviation of ____”.
--------------------------------------------------------------------------------------------------------------------------------------Identify the choice that best completes the statement or answers the question.
1. If a population has a standard deviation 𝜎, then the standard deviation of the mean of 100 randomly selected
items from this population is
a. 𝜎
b. 100𝜎
𝜎
c. 10
d.
𝜎
100
e. 0.1
2. Suppose we are planning on taking an SRS from a population. If we double the sample size, then 𝜎𝑥̅ will be
multiplied by:
a. √2
b.
1
√2
c. 2
1
d. 2
e. 4
A factor produces plate glass with a mean thickness of 4 millimeters and a standard deviation of 1.1 millimeters. A
simple random sample of 100 sheets of glass is to be measured, and the sample mean thickness of the 100 sheets 𝑥̅ is to
be computed. The probability that the average thickness 𝑥̅ of the 100 sheets of glass is less than 4.1 millimeters is
approximately..
b. 0.8186
b. 0.3183
c. 0.1814
d. 0.6917
Identify variables, draw pictures and show all work.
3. The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution
over the interval from 0 to 2 minutes. It can be shown that for this distribution 𝜇 = 1 and 𝜎 = 0.3.
a. What is the probability that a random individual will have a wait of more than 90 seconds for the
elevator?
b. What is the probability that a random sample of 40 individuals will have a mean wait of more than 90
seconds for the elevator?
4. The weights of newborn children in the United States vary according to the normal distribution with mean 7.5
pounds and standard deviation 1.25 points. The government classifies a newborn as having low birth weight if
the weight is less than 5.5 pounds.
a. What is the probability that a baby chosen at random weighs more than 5.5 pounds at birth?
b. If you choose three babies at random and compute their mean weight, 𝑥̅ , what is the mean and
standard deviation of the mean weight 𝑥̅ of the three babies?
c. What is the probability that their average birth weight is less than 5.5 pounds?
d. Would your answer to part c be affected if the distribution of birth weights in the population were
distinctly non-normal?
5. Information on a packet of seeds claims that the germination rate is 92%. If a packet contains 160 seeds, what is
the probability that more than 95% of the seeds will germinate?
a. Name the population and the sample.
b. Can we use the formula for standard deviation? Why?
c. Can we use normal distribution? Why?
d. Find the mean and standard deviation of the sample.
e. Do the calculation. (Yes – that means a picture too! )
f.
Conclusion?