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?

PSY-520 Graduate StatisticsTopic 3 – Benchmark – Correlation and Regression ProjectDirections: Use the following information to complete the questions below. Use the following data points that have a linear relationship: Substance Abuse and Suicide: Percent of the Total U.S. PopulationX VARIABLEY VARIABLEYearSubstance UseSuicides19996.820.00010520006.780.00010420017.000.00010720027.120.0001120037.090.00010820047.050.0001120057.170.00010920067.240.0001120077.280.00011320087.360.00011620097.800.00011820107.810.00012120117.880.00012320127.870.00012520138.070.00012620148.120.0001320158.060.00013320168.170.00013420178.180.0001420188.230.000142Run a bivariate correlation on Substance Use and Suicides. Report the Pearson correlation coefficient. Find a linear model of the relationship between the X and Y variables and report the regression line. Provide an output of the SPSS results and interpret the results using correct APA style. In 300-500 words, address the following: Identify the predictor variable and the criterion variable. Describe the relationship between Substance Use and Suicides in terms of strength (weak/strong) and direction (positive/negative). Discuss whether you can make cause and effect statements when you get a significant correlation.