1. (4 points) A college is conducting a study to determine if it should switch to a new Learning Management System (LMS). Students that agreed to participate in the study must conclude with a "Yes" or "No" in favor or against the assigned LMS. Out of the 680 students that were involved in the study, 306 were assigned to the current BoardLMS, and the rest were assigned to SpaceLMS. Among those assigned to BoardLMS, 52% concluded with a "Yes". However, 63% of those assigned SpaceLMS concluded with a "Yes". a. (2 points) If a randomly selected student from the sample happened to conclude with a "No" decision, find the probability that the student is assigned to SpaceLMS. b. (2 points) If a student that was selected at random concluded with a "Yes" decision, determine the probability that the student is assigned to BoardLMS. 1. The sample mean x of observations x1, x2,..., x is given by: 2. Sample median: x= (n+1)th ordered values average of (4)th and (+1)th ordered values 71 when n is odd when n is even 3. Sample variance: 5 = (x-x) n-1 Lxf- (Px1)2 or 72 n-1 4. Fourth spread (Interquartile range) = fs= upper fourth - lower fourth 5. Any observation farther than 1.5fs from the closest fourth is an outlier. An outlier is extreme if it is more than 3fs from the nearest fourth, and it is mild otherwise. 6. Let denote the null event. When An B=0, A and B are said to be mutually exclusive or disjoint events. - 7. P(A UB) = P(A) + P(B) = P(A n B) 8. P(A') = 1-P(A) 9. P(A U A') = P(S) = 1 10. P(A) = N(A) N Number of outcomes containing A Total number of outcomes in the sample space n! 11. Combination: () = k!(n-k)! 12. Conditional probability of A given B: P(A|B) = P(ANB) P(B) 13. The multiplication rule: P(A n B) = P(A|B).P(B) 14. The Law of Total Probability: Let A1, ..., Ak be mutually exclusive and exhaustive events. Then for any other event B: P(B\A)P(A) + P(B\Ak)P(A) = P(BIA)P(A) =1 15. Bayes' Rule formula: P(A|B) = = P(AjB) = P(BA)P(A) j = 1, ..., k P(B) i=1 P(B|A)P(A) 16. Two events A and B are independent if P(A|B) = P(A) and are dependent otherwise. 17. If A and B are independent, P(AnB) = P(A). P(B)