Business Administration, Assignments of Organization and Business Administration

Download Business Administration and more Assignments Organization and Business Administration in PDF only on Docsity! ASSIGNMENT No. 1 Course: Applied Math for Business & Social Sciences (8405) Semester: Autumn, 2020 Level: BBA (4 years) Q. 4 Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars accounted for 18% of the vehicles on the road, but accidents involving small cars led to 11,898 fatalities during a recent year. Assume the probability a small car is involved in an accident is .18. The probability of an accident involving a small car leading to a fatality is .128 and the probability of an accident not involving a small car leading to a fatality is .05. Suppose you learn of an accident involving a fatality. What is the probability a small car was involved? Assume that the likelihood of getting into an accident is independent of car size. The task state following probabilities in case of traffic accidents: P(small car) = 0.18 P(accident | small car) = 0.18 P(fatality |small car) = 0.128 P(fatality | not small car) = 0.05 Use the complement rule to define the probability of not having a small car P(notA) = 1 – P (4) Put the known parameter in the rule: P(not small car)= 1 - 0.18 = 0.82 Since the events of Accidents are independent of the car size rule sets following: P (accident | small car) = P (accident | not small car) P( accident | not small car ) = 0.18 Bayes’ theorem says: First compute the probability of all accident involving a fatality: P(S) = P (accident | small car) . P (fatality | small car) = 0.18 x 0.128 = 0.02304 P(B) = P (accident |not small car) P (fatality | not small car) = 0.18 x 0.05 = 0.009 2 Follow the Bayes rule and compute: Q. 2 Solve the following second degree inequalities: a) 4x2 -100 < 0 b) 2x2+5x+3 < 0 a) 4x2 -100 < 0 4(x2-25)<0 x2-25<0 x€ (5,5) b) 2x2+5x+3 < 0 2x2+2x+3x+3 < 0 2x(2x2/2x + 2x/2x) + (3x/3 + 3/3)<0 x€(-3/2 , -1) Q. 3 Calculate the corner points of the feasible region: 3x + 2y 15 6x+ 9y > 36 y>-2/3x + 4 6x + 9y >36 (6x + 9y) + (-36) >36 + (-36) 6x + 9y -36 > 36 -36 Y > -2/3x + 4