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:

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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