According to recent research by NASA, 28% of the world's space products are manufactured in the USA. Consider a random sample of five space products and let x represent the number in the sample that are manufactured in USA. The formula below gives the probability distribution for x, where n! = (n)(n – 1)(n - 2...(2)(1). Complete parts a through d. (51)(0.28)*(0.72)5 - × p(x) = (x!)(5 – x)! a. Explain why x is a discrete random variable. O A. The event x is a discrete random variable because the values of the random variable are contained in one or more intervals. O B. The event x is a discrete random variable because the values of the random variable are countable. OC. The event x is a discrete random variable because the values of the random variable are countable and each possible outcome is equally likely. O D. The event x is a discrete random variable because the values of the random variable are contained in one or more intervals and each possible outcome is not equally likely. b. Find p(x) for x=0, 1, 2, 3, 4, 5. 1 2 3 4 5 p(x) (Type integers or decimals rounded to three decimal places as needed.) c. Check that the properties for a discrete probability distribution are satisfied. Select all that apply. O A. Each probability is greater than or equal to 0. O B. The probabilities sum to 0. O C. Each probability is greater than or equal to 1. O D. The probabilities sum to 1. O E. The properties for a discrete probability distribution are not satisfied. d. Find the probability that at least three of the five space products in the sample are manufactured in USA. P(x2 3) =D (Type an integer or a decimal rounded to three decimal places as needed.)