ect Question 1 0 / 10 pts Given the following probability distribution X 0 1 2 3 P(x) 0.4 0.3 0.2 0.1 Find the probabilities: (a) P("X is odd") (b) P("X 2 1"). O (a) 0.6 (b) 0.5 O (a) 0.4 (b) 0.3 O (a) 0.4 (b) 0.6 O (a) 0.5 (b) 0.6ect Question 3 0 / 10 pts Refer to question 1. Find (a) the variance (b) the standard deviation. O (a) 0.9 (b) 0.95 O (a) 1 (b) 1 O (a) 0.9 (b) 0.3 O (a) 0.64 (b) 0.8Question 4 10 f 10 pts A dust mite allergen level that exceeds 2 micrograms per gram {pgfg} of dust has been associated with the development of allergies. Consider a random sample of four homes and let X be the number of homes with a dust mite level that exceeds 2 pgfg. The probabilityr distribution for X, based on a studv. is shown in the following table. 0 1 2 3 4 0.439 0.3:} 0.3? 0.24:: 0.04 Find the probability that fewer than two homes in the sample have a dust mite level that exceeds 2 \"gig. Question 5 1' 1\" \"1'5 Refer to question 4. Find the mean I-lx- Queson 6 0 f 10 [m Refer to question 4. Find the standard deviation ox. 0.9993. You selected this answer. ect Question 7 0 / 10 pts Refer to question 4. Find the exact probability that X is in the interval u + 20, i.e., find the probability P(u - 20 < X < u + 20). Compare the Empirical rule. O 0.99 O 0.95 0.96 O 0.98Suppose 30% of trees in a forest are infected with a parasite. Four trees are randome sampled. Let X denote the number of the trees sampled that have the parasite. Determine the probability:r distribution of the random variable I. Use the probability distribution of X to nd the pnababilitinr P{[}i = 1]]. 9"? Question 9 u 1" 111 [1125 Refer to question 3. Calculate the mean of X: i-lx- Question 10 0 f 10 PE Refer to question 3. Calculate the standard deviation of X: ox