Download Math 201 - Statistical Methods

Math 201 - Statistical Methods
Practice Mid-Term Exam 1
You are allowed to use a single standard-sized sheet of notes on this exam. The notes must be original copies,
handwritten by you, and may be on both sides of the sheet. You must turn in your page of notes with your
exam.
You must bring a calculator to use on this exam. The calculator must be able to perform basic arithmetic
operations: addition, subtraction, multiplication, division, exponentiation, and square root. You may only use
standalone calculators and not calculators that are part of other communication devices. Although calculators
with more advanced features are not explicitly prohibited, you will not receive credit for unjustified responses
to problems which require more than the basic arithmetic operations.
The use of communication devices or other unauthorised materials during this exam constitutes a violation
of academic integrity.
You will have 70 minutes to work on this exam.
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Problem 1
Consider the following data set:
14, 15, 15, 16, 19, 20, 20, 21, 25, 42, 78, 84, 100
(a) Circle one that describes this data:
unimodal
bimodal
(b) Circle one that describes this data:
skewed to the left
symmetric
skewed to the right
(c) What is the mean?
(d) What is the median?
(e) What is the 25th percentile?
(f) What is the third quartile?
(g) What is the interquartile range?
(h) What are the possible outliers?
(i) What are the probable outliers?
(j) Draw a box-and-whisker plot for this data. Extend the whiskers out to the most extreme observations
which are not outliers. Indicate possible outliers with × and probable outliers with +.
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Problem 2
The height of adult men has mean 177 centimeters and standard deviation 7 centimeters. The probability
that a randomly chosen man has height between 170 centimeters and 184 centimeters is 0.68. The weight of
adult men has mean 83 kilograms and standard deviation 12 kilograms.
(a)
(b)
(c)
(d)
(e)
A height of 173 centimeters corresponds to what z-score?
A z-score of −0.2 corresponds to what weight?
What is the variance for the weight?
What is the coefficient of variation for the weight?
If 5 men are chosen at random, what is the probability that at least 4 of them have height between
170 centimeters and 184 centimeters?
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Problem 3
Suppose that, each day, there is a 40% chance that the temperature will be hot and a 60% chance that the
temperature will be cold. Each day, there can be either rain or snow, but not both, or there could be no
precipitation at all. On the hot days, there is a 70% chance of rain, a 0% chance of snow, and a 30% chance
of no precipitation. On the cold days, there is a 50% chance of rain, a 20% chance of snow, and a 30% chance
of no precipitation.
(a) Circle two events which are independent:
hot
cold
rain
snow
no precipitation
(b) Circle two events which are complementary:
hot
cold
rain
snow
no precipitation
(c) Circle two events which are mutually exclusive but not complementary:
hot
cold
rain
snow
no precipitation
(d) What is the probability that a day is both cold and rainy?
(e) What is the probability that a day is both hot and rainy?
(f) What is the probability that a day is rainy?
(g) Given that a day is rainy, what is the probability that the temperature is hot? Hint: Use Bayes’s
Theorem.
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Problem 4
Suppose you roll a single six-sided die. Let X be the random variable representing the square of the result.
For instance, if the die lands on a 4, X would be 16.
(a)
(b)
(c)
(d)
(e)
(f)
What
What
What
What
What
What
are the possible values of X?
is the probability distribution of X?
is the probability that X is less than 23?
is the expected value of X? Round this result to the nearest tenth before proceeding.
is the variance of X?
is the standard deviation of X?
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