Mode and Median probability, statistics homework help
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?