Mode and Median probability statistics homework help

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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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