A rаndоm vаriаble x represents the number оf pets оwned by a household. Assume that x can take on five values: 0, 1, 2, 3, 4. A partial probability distribution is shown below: (7 pts; 1 pt each) X 0 1 2 3 4 P(X) 0.15 0.25 ? 0.20 0.05 a. Find the probability that a household owns two pets. b. Calculate the mean. c. Calculate the standard deviation. d. What is the probability that a household owns more than two pets? e. What is the probability that a household owns at most 3 pets? f. Find the probability that a household owns between 1 and 3 pets, inclusive. g. Find the probability that a household owns no more than one pet.
Answer the fоllоwing questiоns. а. It is believed thаt 52% of college students prefer online clаsses over in-person classes. Assuming this to be the case, what is the probability that at most 109 students prefer online classes in a random survey of 200 college students? (3 pts) b. A box of 12 light bulbs contains 4 defective bulbs and 8 working bulbs. You randomly select and purchase three of these bulbs. What is the probability that exactly two of the bulbs you selected are working? (2 pts) c. About 70% of commuters in a city use public transportation. Suppose that five randomly selected commuters are interviewed. What is the probability that at least one commuter does not use public transportation? (2 pts) d. An event planner must set up two banquet rooms. Each room must have a table arrangement, a centerpiece, a lighting setup, and two chair styles. At a local rental company there are 5 table arrangements, 7 centerpieces, 3 lighting setups, and 8 chair styles, all of which are compatible. How many choices does the planner have if she wants to select two table arrangements, two centerpieces, two lighting setups, and four chair styles if she doesn't want to select more than one of any model? (2 pts) e. A committee chair must select four members from a pool of nine volunteers to attend a conference. If all funds are to be used (i.e., four members will go), how many different groups can the chair select? (2 pts) f. Marcus frequents one of two gyms, choosing Gym A 40% of the time and Gym B 60% of the time. At Gym A, he takes a spin class on 30% of his visits. At Gym B, he takes a spin class on 70% of his visits. Marcus goes to a gym and takes a spin class. What is the probability that he is at Gym B? (4 pts)