1.
Read the webpage, https://en.wikipedia.org/wiki/Binomial_distribution , down to the
section, Mode and Median. Read
thoroughly the example about the biased coin that comes up heads with
probability of 0.3. This variable can be
described as, X~Bi(n=6, p=0.3). Use this
example to answer the following questions.
a.
What is the expected value of this variable?
b.
What is the expected number of heads if this coin is tossed
6 times? Same answer as in part 2.a. but
in different words.
c.
What is the probability that the number of heads out of 6
tosses of this unfair coin is less than 2?
d.
What is the probability that the number of heads out of 6
tosses of this unfair coin is more than 2?
e.
What is the probability that the number of heads out of 6
tosses of this unfair coin is at least 2?
f.
What is the probability that the number of heads out of 6
tosses of this unfair coin is at most 2?
2.
Assume that 25% of all accounting audits identify an
accounting error and that 8 audits were completed. The variable of interest is the number of
audits that identify an accounting error out of the 8 audits. The distribution of this variable is
described as X~Bi(n=8, p=0.25). Use this
information to answer the questions below.
Use this online calculator, if you want:
com/online-calculator/binomial.aspx”>http://stattrek.com/online-calculator/binomial.aspx
a.
What is the expected number of audits that will identify
accounting errors?
b.
What is the probability of 2 or more accounting errors being
identified in the 8 audits?
c.
What is the probability of 3 or more accounting errors being
identified in the 8 audits?
d.
What is the probability of 4 or more accounting errors being
identified in the 8 audits?
e.
What is the probability of 5 or more accounting errors being
identified in the 8 audits?
f.
What is the probability of 6 or more accounting errors being
identified in the 8 audits?
g.
What is the probability of 7 or more accounting errors being
identified in the 8 audits?
h.
What is the probability of 8 or more accounting errors being
identified in the 8 audits?
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