Please answer the three problems. Complete the task in each problem. Show your complete solution in each problem. Thank you so much!

1. A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. X P(x) 0.15 0.35 N 0.40 0.10 a. Define the random variable X. b. What is the probability the baker will sell more than one batch? P(x > 1) = c. What is the probability the baker will sell exactly one batch? P(x = 1) = d. On average, how many batches should the baker make? 2. a. Complete the expected value table, find the expected value and standard deviation from the given data. b. Sketch a graph of the probability distribution of X. x P(x) x . P(x) (x - H)2 . P(x) 0.15 0.25 N 3 0.30 0.20 5 0.10 Total 3. Functional literacy refers to the capacity of a person to engage in all those activities in which literacy is required for effective function of his or her group and community and also for enabling him or her to continue to use reading, writing and calculation for his or her own and the community's development. About 91.6 percent Filipinos 10 to 64 years old were functional literate l in 2019, according to the results of the 2019 Functional Literacy, Education and Mass Media Survey (FLEMMS). This translates to around 73.0 million out of 79.7 million in the same age group who are considered literate on a functional level. Suppose you choose 5 people at random. Let X = the number of people who are literate. a. Using the formulas, calculate the (i) mean and (ii) standard deviation of X. Interpret the result. b. Find the probability that more than five people in the sample are literate. Interpret the result