Flag question: Question 1 Question 1 17 pts A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article "Pathological Video Game Use among Youths: A Two-Year Longitudinal Study" (Pediatrics, Vol. 127, No. 2, pp. 319-329) by D. Gentile et al., in 2011, about 9% of children in grades 3-8 were PVGUs. Suppose that, today, five youths in grades 3-8 are randomly selected. Let X represent the number of youths who are PVGUs. n = p = 1 - p = 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 5 =1.0000 = 1.0000 Calculate the probability that EXACTLY three youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X = 3) = Calculate the probability that AT LEAST two youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X 2) = Calculate the probability that AT MOST three youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X 3) = Calculate the probability that BETWEEN two and four youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(2 < X < 4) = Calculate the probability that BETWEEN two and four (INCLUSIVE) youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(2 X 4) = Calculate the mean of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. E(X) = = Calculate the variance of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. 2 = 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 According to Injury Facts, a publication of the National Safety Council, in the United States, the lifetime probability of dying in a motor-vehicle crash is 1 in 108. Suppose that 200 deaths were randomly selected. Let the number of deaths due to motor-vehicle crash be represented by the random variable, X. n = = (Round your asnwer to TWO decimal places, e.g., X.XX) Calculate the probability that none of the deaths are due to motor-vehicle crash. Round your answer to four decimal places, e.g., 0.XXXX or .XXXX. P(X = 0) = Calculate the probability that three or more of the deaths are due to motor-vehicle crash. 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. =