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.aspxa. 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?

1-1 Discussion: Population, Samples, and BiasIn real-life applications, statistics helps us analyze data to extract information about a population. In this module discussion, you will take on the role of Susan, a high school principal. She is planning on having a large movie night for the high school. She has received a lot of feedback on which movie to show and sees differences in movie preferences by gender and also by grade level.She knows if the wrong movie is shown, it could reduce event turnout by 50%. She would like to maximize the number of students who attend and would like to select a PG-rated movie based on the overall student population's movie preferences. Each student is assigned a classroom with other students in their grade. She has a spreadsheet that lists the names of each student, their classroom, and their grade. Susan knows a simple random sample would provide a good representation of the population of students at their high school, but wonders if a different method would be better.You can review the student demographics here: Module One Discussion Data.In your initial discussion post, specifically address the following:Introduce yourself and describe a time when you used data in a personal or professional decision. This could be anything from analyzing sales data on the job to making an informed purchasing decision about a home or car.Describe an example of a sample of this student population that would not represent the population well.Describe another example of a sample that would represent the population well.Finally, describe the relationship of a sample to a population and classify your two samples as random, cluster, stratified, or convenience.In your response posts to at least two peers, discuss the following:Choose two different sampling methods from among your peers' responses. Then, identify bias in each peer's sample and explain how you think they could remove it