W Content Let's approach the proportionality of black or African-American inmates in Polk County Jail a little differently. Submit a post to this discussion with your answers and details to the following: 1. Uisemgle to find the percent of black or AfricanAmerican people living in Polk County, IA. What percent didvyou nd? In a . perfect world, we would expect the same percent of black or African-American inmates in Polk County Jail, This percentage Will also serve as the value of p, the probability an inmate selected at random is black or African-American. Paste a link for the source of your data. . Now go to the website of current inmatesrecoi'dod by theiEorlkVCounty Sheriifcc. Select two separate days (preferably a weekday and weekend) and perform a census of all inmates from those two days (cluster sampling). What were the days you selected (include date and day of the week)? How many total inmates occurred from the two days you selected? This number will also sen/e as your number of trials n. . Inspect the Details of each inmate from the two days you selected. How many were black orAfrican-American? This number will also serve as a cutoff value for your random variable x (the number of black or African-American inmates from a sample of inmates). . Using your value of n (from step 2) and p (from step 1), calculate the expected (or mean) number of black orAfrican-American inmates out of a total of n inmates Recall that the mean equals n times p. n=11-p Also calculate the standardrdeviation number of black or African-American inmates out of a total of n inmates. Recall that the standard deviation equals ]he square root of n times p times 1 minus p. azi/rznpwlp) . What is the cutoff number of black or African-American inmates that would be considered significantly low (the mean minus 2 standard deviations or [A 20) OR significantly high (the mean plus 2 standard deviations or y + Zn)? Did your own cluster sample have a significantly low or high number of black or African-American inmates? . Next, we are interested in calculating how much different x black orAfrican~American inmates (from step 3) are from what we would expect (from step 4). a. If your value of x is less than or equal to the mean, calculate the binomial probability of x successes or less. b. if your value of x is greater than the mean, calculate the binomial probability of x successes or more. Complete only the part above that applies to your own value of x. For example, suppose you found p=.068 (step 1), sampled n=11 (step 2), and calculated a mean (step 4) of 0.75. If you counted x=3 (step 3) inmates that were black orAfrican-American, then you would fall under case b from above. You would want to calculate the binomial probability of P(X Z 3) . i would recommend using StatCrunch to calculate this probability using the Binomial Calculator (select Stat > Calculators > Binomial within StatCrunch). Post a screenshot of the binomial calculator with your results. *3 l. y W 28F Mostlyclear A x Home - myDMACC x W Content dmacc.blackboard.com, tili.' ' i'iO7093j/cl/outline CU Press Enter or Compute to update. - A musKase ~81 ' .335 % ii i? n [H D: .068 l f P(x \"2 H3 )4 :2 Compute 4?\" You'll input your sample size n from step 2, probability p from step 1, number x from step 3, and correct inequality from step 6. . Once you click the Compute button, you'll get the binomial probability you are looking for 7. Recall that any event with a likelihood of less than 5% is commonly interpreted as statistically significant. Based on this 5% threshold, are your x black or African-American inmates (based on the probability you calculated from step 6) statistically i significant, or are they about what we would expect? 8. This experiment does satisfy the four requirements of a binomial distribution. Explain how each requirement is met. a. fixed number oftrials n ' xii\" mu b. independence of trials c. constant probability of success with each trial l l I, d. only two possible outcomes (success and failure) with each trial _ i 9. Finally, comment on at least two other students' posts for full credit on this discussion board assignment. Comments such as \"good job\" are not productive. Try to be more specific by comparing and contrasting their results with your own. NOTE: Before you are allowed to view other students' posts to this discussion board, you must first submit your own. Empty 1 .6 :' I ii in. i v a e 6' 28F Mostlyclear A (1* Q E fr; a} V