The University of the South Pacific Faculty of Science, Technology & Environment School of Computing, Information and Mathematical Sciences MA101: Mathematics for Social Science, Semester 1, 2016 Assignment 2 Due Date: 15/05/16, (11.55pm) Total: 40 marks Instructions: 1. Please complete this assignment and upload your solution in the assignment drop box on Moodle before the due date. 2. Write your name, ID and your Campus on the cover page of your assignment. 3. Plagiarized assignment will be awarded a mark of 0. Question 1 [3 + 8 + 4 = 15 marks] A) Through a mix-up on the production line, 21 defective ovens were shipped out with 29 good ones. If 8 are selected at random, what is the probability that none of them are defective? B) Calculate the mean, median and standard deviation of the given sample data. C) Scores Frequency 0 - 10 4 10 - 20 8 20 - 30 10 30 - 40 12 40 - 50 6 A survey of 50 lobster fishermen on Funafuti (an island in Tuvalu), found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. If a fisherman is selected randomly, what is the probability that his catch is less than 20 pounds? Question 2 [5 + 5= 10 marks] A) 1 , x 0 2 For what values of x is the function h x x 2 , 0 x 4 discontinuous? 2 x 12, x 4 B) Find the derivative of f ( x) x3 using the definition of the derivative. Question 3 [7 +8= 15 marks] 1 2 dy if 384, 000 30 x 3 y 3 . dx A) Use implicit differentiation to find B) A fertilizer producer finds that it can sell its product at a price of p 300 x dollars per unit when it produces x units of fertilizer. The total production cost (in dollars) for x units is C ( x) 20,000 24 x 0.5x2 . How many units must be manufactured to maximize the profit? All the Best