Flag question: Question 1 Question 1 17 pts The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Four randomly selected adult Americans are examined for psychiatric disorders. Let the number of adults who suffers from psychiatric disaster be represented by the random variable, X n = p = (Round to 4 decimal places) 1 - p = (Round to 4 decimal places) Prepare the probability distribution for the random variable X. Complete the following table. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. X = x P(X = x) 0 1 2 3 4 =1.0000 = 1.0000 Calculate the probability that EXACTLY three adult American suffer from a psychiatric disorder. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X = 3) = 6. Calculate the probability that AT LEAST one adult American suffer from a psychiatric disorder. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X 1) = 7. Calculate the probability that AT MOST three adult American suffer from a psychiatric disorder. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X 3) = 8. Calculate the probability that BETWEEN one and three adult American suffer from a psychiatric disorder. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(1 < X < 3) = 9.Calculate the probability that BETWEEN one and four (INCLUSIVE) adult American suffer from a psychiatric disorder. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(1 X 4) = 10.Calculate the probability that more than one but no more than four adult American suffer from a psychiatric disorder Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(1 < X 4) = 11. Calculate the mean of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. E(X) = = 12. Calculate the variance of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. 2 = 13. Calculate the standard deviation of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. = Flag question: Question 2 Question 2 6 pts From the U.S. Census Bureau and the article "U.S. Prison Population Falls for Third Year" by B. Montopoli of CBS News, we found that about 1 in every 200 Americans are in prison. Suppose 500 Americans are randomly sampled. Let X represents the number of Americans currently in prison. n = = (Round to two decimal places) Calculate the probability that three of the 500 Americans are currently in prison. Round your answer to four decimal places, e.g., 0.XXXX or .XXXX. P(X = 3) = Calculate the probability that at least three of the 500 Americans are currently in prison. Round your answer to four decimal places, e.g., 0.XXXX or .XXXX. P (X 3) = 1 - P (X < 3) = Calculate E(X) = . Round your answer to two decimal places, e.g., 0.XX or .XX. = E(X) = Calculate the standard deviation of X. Round your answer to two decimal places, e.g., 0.XX or .XX