please put answers in complete sentences.

Exam 2 Review WS DIRECTIONS: SHOW ALL WORK! A final response following a calculation should be a sentence. Place a box around your final response Round probability calculations to 4 decimal places. Round other numerical results including percents to two decimal places (e.g. 2.56 shoes, 18.49%). 1. A random sample of 400 State U faculty members was asked if they support a no-smoking ordinance on campus. Below are the data that also show their rank at the college. Adjunct Asst Assoc Full TOTAL Yes 135 105 34 26 300 No 47 35 10 100 TOTAL 182 140 400 a. What is the probability a faculty member is an adjunct or supports the smoking ban? b. What is the probability a faculty member does not support the smoking ban given he/she is full professor? c. Are the events assistant professor and supports the smoking ban independent? Justify. 2. Suppose 78% of all Dairy King customers order a frozen treat during their visit, 42.5% order an item from the grill, and 33.15% do both. Calculate the following probabilities: a. A randomly selected customer orders a frozen treat or an item from the grill but not both. b. A randomly selected customer orders a frozen treat given he/she ordered an item from the grill. c. Are the events orders a frozen treat and orders a grill item independent? Justify 3. The student senate at State U comprises 28 members. Of these, 10 belong to the Young Republicans. Suppose a group of four student senators will be selected at random. What is the probability the group contains at least one member of the Young Republicans? Interpret this probability in context. 4. Two of the larger dormitories on State U's campus are Williams Hall and International Hall. 84.6% of students who live in Williams Hall purchase the school's meal plan, and 78.3% of students who live in International Hall purchase the school's meal plan. Of the students living in these two dorms, 59.4% live in Williams Hall. What is the probability a randomly selected student lives in International Hall given the student is part of the school's meal plan. 5. The Fellowship of the Ring had a collection of 9 individuals from various races (Hobbits, Elves, Men, Dwarves) in Middle Earth. Let X be the number of men in a random group of 2 members. Below is the probability distribution for X. # men probability 0.5833 0.3889 0.0278 Compute the expected number of men in the group and interpret. 6. Past data indicate 62.8% of all Coruscant residents agreed with the decision by the Galactic Senate to grant the chancellor his emergency powers during the Separatist Crisis. a. If we select residents at random, what is the probability the first one that agreed with the senate occurs before the fifth selection? b. What is the probability it takes from two selections to six selections to find the first resident that agreed with the decision? c. How many residents do we expect to select before finding the first one that agreed with the decision? Interpret this result. d. In a randomly selected group of 25 residents, what is the likelihood at least 14 agreed with the decision? e. In a randomly selected group of 28 residents, what is the likelihood from 13 to 22 agreed with the decision? f. How many residents in a random group of 32 residents do we expect agreed with the decision? Interpret the result. g. Suppose we select a random sample of 870 Coruscant residents. If appropriate, use the sampling distribution of p to estimate the likelihood less than 58.6% of the residents agreed with the decision.7. The property manager at a large apartment complex knows there tend to be 8.7 service calls on average each day during normal business hours (8am-5pm). Compute the likelihood of each event. a. The office receives 12 service calls tomorrow. b. The office receives less than 10 service calls tomorrow. c. More than 264 calls are received during the next month. Assume the month has 30 days. d. Less than 2 hours pass between consecutive service calls. e. Between one and three hours pass between consecutive service calls. 8. A lab rat is set loose in a maze that allows the rodent to exit through a 6-inch doorway. When no food reward is provided at the end, the point at which the rat exits the maze is uniformly distributed on the interval from 0 to 6 as measured from the left side of the doorway. a. Sketch the density curve for the distribution exit locations. Be sure to label appropriately. b. What is the probability the rat exits between 1.25 inches and 3.85 inches from the left side of the doorway? 9. The administration at State U wants to make textbook scholarships available for those most in need. Assume the average household income of a student follows a normal distribution with a mean of $81,275 and a standard deviation of $14,186. The college wants to limit the scholarship to the neediest 4% of students. a. On what interval do we find the middle 70% of household incomes? b. What is the cutoff to qualify for the scholarship? c. In a randomly selected group of 25 students, what is the probability their mean income would be more than $86,720