University of the People MATH 1280B Graded Quiz Unit 8 All correct answers

3/26/2019 Graded Quiz Unit 8

MATH 1280B Introduction to Statistics - Term 3, 2018-2019
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Information
Recall that the population average of the heights in the le "pop1.csv" is μ =
170.035. Using simulations we found that the probability of the sample
average of the height falling within 1 centimeter of the population average
is approximately equal to 0.626. From the simulations we also got that the
standard deviation of the sample average is (approximately) equal to
1.122. In the next 3 questions you are asked to apply the Normal
approximation to the distribution of the sample average using this
information. The answer may be rounded up to 3 decimal places of the
actual value:




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Question 1




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Using the Normal approximation, the probability that sample average of




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Not yet answered the heights falls within 1 centimeter of the population average is




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Marked out of
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1.00 Answer: 0.6272133
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aC s
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Question 2 Using the Normal approximation we get that the central region that
Not yet answered contains 95% of the distribution of the sample average is of the form
Marked out of 170.035 ± z · 1.122. The value of z is
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1.00
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Answer: 1.959964
is




Question 3
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Using the Normal approximation, the probability that sample average of
Not yet answered the heights is less than 168 is
Marked out of
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1.00 Answer: 0.03486




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, 3/26/2019 Graded Quiz Unit 8
Question 4 According to the Internal Revenue Service, the average length of time for
Not yet answered an individual to complete (record keep, learn, prepare, copy, assemble and
Marked out of send) IRS Form 1040 is 10.53 hours (without any attached schedules). The
1.00 distribution is unknown. Let us assume that the standard deviation is 2
hours. Suppose we randomly sample 36 taxpayers and compute their
average time to completing the forms. Then the probability that the
average is more than 11 hours is approximately equal to (The answer may
be rounded up to 3 decimal places of the actual value.) 0.07926984 .




Information
Suppose that a category of world class runners are known to run a
marathon (26 miles) in an expectation of 145 minutes with a standard
deviation of 14 minutes. Consider 49 of the races. In the next 3 questions




m
you are asked to apply the Normal approximation to the distribution of the




er as
sample average using this information. The answer may be rounded up to




co
eH w
3 decimal places of the actual value:




o.
rs e
ou urc
Question 5 The probability that the runner will average between 142 and 146 minutes
o

Not yet answered in these 49 marathons is
aC s


Marked out of
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1.00 Answer: 0.6246553
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ar stu




Question 6 The 0.80-percentile for the average of these 49 marathons is
Not yet answered
is




Marked out of Answer: 146.6832
Th




1.00
sh




Question 7 The median of the average running time is
Not yet answered

Marked out of Answer: 145
1.00


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https://my.uopeople.edu/mod/quiz/attempt.php?attempt=1762319&cmid=169036 2/5
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