In the article posted in Module 4, authored by Sommerteld (with title "The Binomial and Hypergeometric Probability Distributions in Jury Selection," the authors show how the Binomial and the Hypergeometric models can be used to show that a jury panel is biased. A way to do that is to use the population parameter p (probability that an individual in the population has the characteristic of interest) then calculate the probability that in a random sample of size n, we would find a given number of individuals with that characteristic. For example, if in San Joaquin County 5% of the population are African American, and we choose a random sample of size 105 from that population, using the Binomial model we can calculate that the Probability of having 0 African American by chance in the sample is 0.00458, using the binomial formula. You can use the app posted in Module 5 to calculate. https2/[homepagedivms.uiowa.eduj~mbognarlappletsjbin.html The fact that by chance you are not likely to see 0 African Americans in the sample indicates that the panel is biased, not random (of course, statisticians could come up with additional tests to be sure, but probability that low says that if the random sample is really random, that is not possible). With that information given abover what would be the expected number of African Americans in that sample of 105 from San Joaquin County? I: a. 5.25 D b. o I: c. 'I I: d. 'l Let X be the number of bacterial colonies per cubic centimeter, a Poisson random variable with expected value 3. (i) What is the probability that there is at least one bacterial colony in a randomly chosen cubic centimeter\"? (ii) What is the probability that in five randomly chosen cubic centimeters there is at least one cubic centimeter where there is at least one bacterial colony? (iii) How many cubic centimeters must be observed for the probability of observing at least one with at least one bacterial colony to be 0.95? What is the probability that there is at least one bacterial colony in a randomly chosen cubic centimeter? Choose". A What is the probability that in five randomly chosen cubic centimeters there is at least one cubic centimeter where there is at least one bacterial colony? Choose... How many cubic centimeters must be observed for the probability of observing at least one with at least one bacterial colony to be 0.95? J Choose... 0.9502 07231 5 1 0.9999997 The number alpha particles emitted by a radioactive substance has expected value of 12 per square centimeter. It two 1-square centimeter samples are independently selected, find the probability that two received 4 alpha particles. How many 1-squarecentimeter samples should be selected to establish a probability of approximately 0.95 that at least one will contain one or more alpha particles? If two 1-square centimeter samples are independently selected, find the probability that two received 4 alpha particles. Choose... 0 How many 1-squarecentimeter samples should be selected to establish a probability of approximately 0.95 that at least one will contain one or more alpha particles \\/ Choose... 12 approximately 0 approximately 1