200 people tested positive for COVID-19 were selected to find out if a new created vaccine makes a difference. The people were divided in two groups, 100 each. One group received the vaccine and the second group did not (control group).
Is this an observational study or an experiment?
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Give an example of Descriptive Statistic and Inferential Statistic.
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Construct a stem-leaves plot for the following set of numbers:
71 90 116 76 93 84 69 87 102 70
72 97 72 91 118 101 95 83 80 105
63 88 96 94 92 79 83 102 107 99
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An analysis of train derailment incidents identified the main causes listed below,
where T denotes bad track, E denotes faulty equipment, H denotes human error,
and O denotes other causes.
Construct a frequency table, and include a column
for relative frequencies expressed as percentages.
H T T E H H T H T E H T E H H O O H T H
H E O O T H H O E E E H H E H E T E O T
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Based on this Box Plot Graph, answer the following questions:
a) What percent of data falls in the interval [5,8]? Explain.
b) What percent of data falls in the interval [3,8]? Explain.
c) What interval contains more data: [2, 3] or [4, 5]? Explain.
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Use weighted mean to calculate GPA score for a student
who has the following results for the taken courses:

Show your work.
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5 people from the list of 30 should be selected to participate in survey.
Describe how you will select these five people using systematic sampling technique.
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Find the probability of rolling two dice and have the sum of two numbers on the top 8?
Show your work.
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This exercise involves a complimentary event.
Find the probability of drawing one card from a standard deck
of 52 playing cards so that selected card will be NOT a Queen.
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Calculate Permutation ₁₀P₃ and Combination ₁₀C₃ .
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The following table summarizes data from some company:

What is the probability that randomly selected employee will be
a) Male and Single?
b) Female or Married?
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Find the mean, median, and mode for the set of numbers listed below.
21, 29, 12, 14, 15, 25, 24, 25, 31, 16, 10, 18
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Find the variance and standard deviation for the given set of sample data
(the same as in #12). Show work.
21, 29, 12, 14, 15, 25, 24, 25, 31, 16, 10, 18
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The histogram on the right side shows histogram constructed
from the group of the people participated in a testing.
How many people participated in this test?
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Use Rule 68-95 to evaluate (in %) the shaded area under the normal distribution curve
between x=-s and x= 2s.
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Results of the test are normally distributed with a mean m = 80
and a standard deviation s = 15.
Find probabilities that
a) The score is less than 70.
b) The score is greater than 65.
c) The score is between 65 and 95.
(Round results to three decimal places).
You can use Online Applet for Normal distribution
http://onlinestatbook.com/2/calculators/normal_dist.html
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Use online applet for Standard Normal Distribution
https://homepage.stat.uiowa.edu/~mbognar/applets/normal.html ( m = 0, s = 1 )
to find area under the curve to the left of z = 0.8
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Use online applet for Standard Normal Distribution
http://davidmlane.com/hyperstat/z_table.html (m = 0, s = 1 )
and find for what z-value area under the curve on the right side is 0.22?
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Normal distribution has mean m = 70 and a standard deviation s = 10.
Assume that samples of size n are taken from the whole population and
distribution of samples mean was created.
What will be the mean and standard deviation of that distribution
if all taken samples have size:
a) n = 16
b) n = 64
(Tip: apply Central Limit Theorem).
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A continuous random variable is normally distributed with a mean of 400 and a standard deviation of 50.
Then multiple samples with size 25 were taken. Find the probability that the samples mean will be:
a) less than 385
b) greater than 410
(Tip: find standard deviation of sample mean and then use Applet for Normal distribution http://onlinestatbook.com/2/calculators/normal_dist.html ).
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