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# FSU - STA 2171 - Class Notes - Week 10

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FSU - STA 2171 - Class Notes - Week 10

This preview shows pages 1 - 2 of a 4 page document. to view the rest of the content Recommended Problems:Fourth Edition: 2.3.1, 2.3.2, 2.3.5, 2.3.11,
2.4.5, 2.4.3, 2.6.3 Fifth Edition: 2.3.1, 2.3.2. 2.3.5, 2.3.11, 2.4.5, 2.4.3,
2.6.3
Problems to be turned in:Fourth Edition: 2.2.1, 2.4.2, 2.3.12, 2.6.11Fifth
Edition: 2.2.1, 2.4.2, 2.3.12, 2.6.11Complete the following problems as
well. Note that no work is to be done on these pages.1.Suppose a
constant, say a, is added to every value of a data set. Exactly how does
this affect the mean, variance, and standard deviation when compared to
the originals? Why? (No mathematical proof is needed.)2.Calculate the
standard deviation of the following by hand (show all your work to
receive full marks.):6, 12, 11, 13, 8, 103.Calculate the mean and
standard deviation of each of the following samples by either calculator
or computer:(i) 33, 37, 34, 38, 35, 44(ii) 33, 37, 34, 38, 35, 44, 14(iii)
58, 70, 93, 92, 68, 574.A ficticious sample was taken on FSU’s campus
to find students’ preferences of beverage in the morning. Use the
following table to create a segmented bar chart.
EC. 1  Prove that the sum of all deviations is always equal to zero. (Hint: Think
of the defiinition of the mean)E.C. 2Use R software to create a
histogram and boxplot using the data from problem 2.6.11 For full credit
make sure to include labels. The options “xlab,” “ylab,” and “main” will
Recommended Problems:Fourth Edition: 3.2.7, 3.3.3, 3.6.2, 3.6.6, 3.6.7,
4.3.1, 4.3.9 Fifth Edition: 3.2.8, 3.3.3, 3.6.3, 3.6.8, 3.6.9. 4.3.1, 4.3.9
Problems to be turned in:Fourth Edition: 3.3.1, 3.3.2, 4.3.3Fifth Edition:
3.3.1, 3.3.2, 4.3.3Complete the following problems as well. Note that no
work is to be done on these pages.1.Suppose P(A or B) = 0.22, P(A and
B) = 0.01 and P(B) = 0.12. Find the following(i) Represent this situation
using a venn diagram(ii) P(A|B)(iii) P(B|A)(iv) Are A and B statistically
indepedent? Why?2.Assume that IQ’s are normally distributed with a mean of 100 and standard devation of 15. There are certain
organizations, MENSA for instance, which only allow members that
meet certain criteria. One particular organization only allows members
that are at least two standard deviations above the mean in terms of IQ
score. What percentage of the population can theoretically join this
organization?3.Suppose that X follows a binomial distribution with a
sample size of 40 and a probability of success of 0.75.(i) Find the
probability of getting exactly 39 successes.(ii) Find the probability of
getting at least 39 successes.(iii) Find the probability of getting at least 1
success.4.Use the normal approximation of the binomial distribution to
approximate (ii) and (iii) from exercise 3.5.Suppose that X ∼ N(20,80).
Note that the standard deviation is very large! Find a symmetric interval
about the mean that contains:(i) 90% of the population distribution.(ii)
95% of the population distribution.(iii) 99% of the population
distribution.Note: While Empirical Rule can approximate some of these
for us, we aren’t asked for approximations in this problem.EC. 1Prove
that the sum of the probabilities of all possible events in a binomial
random variable is equal to one. In other words show that
j n − j j=0  p(1−p) =1  STA2171    EC. 2  Complete problem 3 using R. Include your code and results.  Recommended Problems:Fourth Edition: 6.3.5, 6.6.*, 6.7.6, 7.2.4, 7.2.14 Fifth
Edition: 6.3.5, 6.6.*, 6.7.6, 7.2.4, 7.2.14
Problems to be turned in:Fourth Edition: 6.3.6, 6.3.7, 6.7.7, 7.2.3, 7.2.11, 8.2.1,

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