Download Math 120 Exam 3 Review Materials . .

Math 120
Exam 3 Review Materials
Chapter 6
Things to know:
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You should know following about the graph of a normal distribution:
 It is is a bell curve, centered at the mean .
 The curve is symmetrical through a vertical line through the mean.
 The horizontal axis is an asymptote.
 The area under the curve is 1.
 The curve changes from opening down to opening up at the points
and
.
You should be able to sketch a bell curve by hand.
You should know the empirical rule for a normal curve:
 Approximately 68% of the data values lie within one standard deviation of the mean, from
to
.
 Approximately 95% of the data values lie within two standard deviations of the mean, from
2 to
2 .
 Approximately 99.7% of the data values lie within three standard deviations of the mean, from
3 to
3 .
You should be able to use the empirical rule to estimate probabilities. See example 1 on page 275. We
also did some of these in class and you had some on your homework.
Know how to graph a basic control chart.
Do NOT memorize the out—of-control signals (page 279). If you need these on the exam, I will include
them on the formula sheet.
You should be able to convert a measurement x which has a normal distribution with mean and
.
standard deivation to a z-score via
You should know how to find the raw x-score given a z-score.
Know a standard normal distribution has mean
0 and standard deviation
1.
Know how to find the areas under the standard normal curve using the normalcdf(left bound, right
bound, mean, standard deviation) function on your calculator. Also be able to convert an area
statement into a probability statement and include a sketch of the area, just like we did in class.
I will not ask you to use the tables to find areas under standard normal curves.
Know how to use the inverse normal distribution: invNorm(area, mean, standard deviation) to find a zscore or x-score, given an area.
Know how to make a histogram of the distribution. If it is roughly mound-shaped and symmetrical, it is
safe to assume the data follow a normal distribution. See example 10 on page 307.
Know the following terms: population, parameter, sample, statistic.
Know the commonly used statistics and parameters (mean, standard deviation, variation, and
proportion) listed in the box on the top of page 315.
Understand that the sample mean ̅ is a random variable and has a probability distribution. This
distribution is called the Sampling Distribution of the Mean.
Understand Theorem 6.1 on page 320. Know that if x has a normal distribution then the distribution
for ̅ is approximately normal with mean
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̅
and
√
.
Understand the Central Limit Theorem on page 322. Especially know that typically if
distribution for ̅ is approximately normal with mean
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̅
̅
and
̅
√
.
Understand the difference between a single score x and the mean of a sample ̅ .
30 the
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Know how to compute a normal approximation to the binomial distribution. And know when it is
allowed, which means when both are true:
5 and
5.
Know how to make the continuity correction to a normal approximation to the binomial distribution.
Chapter 6 Review Problems: these are on pages 344-347. Do problems odds 1-25 odds to study.
Chapter 7
Things to know:
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A point estimate of a population parameter is an estimate using a single number.
The point estimate of is ̅ .
The point estimate of is ̂ .
Know how to find critical values given a confidence level . Make sure you know how to do this using
your calculator.
Know how to find the confidence interval for mean when is known.
Know how to find the confidence interval for mean when is unknown. And also know to pay
attention to the problem to determine whether is known or unknown.
Write your confidence interval as ̅
̅
.
Make sure you know how to correctly interpret the confidence interval in words (a complete sentence in
terms of the problem).
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Know how to find the sample size
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Have a working knowledge of the t-distribution. Make sure you know the basic properties of the tdistribution listed in the box on page 375. Always pay attention to
1.
Know how to find critical values for the t-distribution either using the table or using the4: InvT
distribution function on your calculator (in the DISTR submenu).
Know how to find a confidence interval for a population proportion . Remember you must check that
both ̂ 5,
5.
Know how to find the sample size for estimating a proportion .
when both and are known.
Know how to find a confidence interval for
Know how to find a confidence interval for
when both and are unknown.
, independent samples. Remember you must check
Know how to find a confidence interval for
5,
5,
5,
5.
that all are true:
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for estimating
when
is known:
Chapter 7 Review Problems: these are on pages 424-427. Do problems odds 1-17 odds to study.