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# GEM2900 Semester II Assignment 2

AU

GPA 3.8

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Date Created: 11/13/15

Available Solution 1000 GEM2900 Semester ll Assignment GEM2902015 Semester ll Assignment 2 Instructions This is the second of a series of assignments for this module Each correct answer to a question is worth two 2 marks This question sheet is available from the module workbin folder Please make sure that you submit your answers via the IVLE assessment facility Submission period Wednesday 1 Apr 1200 hrs to Wednesday 8 Apr 1200 hrs A maximum of two attempts will be allowed for this assessment However if you have made two attempts only the last attempt to this assessment will be graded Exercise 1 There are 40 multiple choice questions in a history test For each question there are 5 alterna tives of which only one alternative is the correct answer 3 marks are awarded for each correct answer and 1 mark is deducted for each wrong answer Little John is taking this history test However he is not fully prepared For each question little John either knows the answer or he doesn39t If he doesn39t then he will guess the answer at random Suppose that he knows the answer to each question with probability 055 It is assumed that he answers each question independently and attempts all the questions Let the random variable X denote the number of questions he answers correctly Then X is a Binomial distribution with parameters n and p Round your answer to two decimal places For example 300 312 010 Exercise 2 Little John39s expected score in the test mentioned in Exercise 1 is Round your answer to two decimal places For example 300 312 010 Exercise 3 A life insurance company estimates that the probability that an individual in a certain risk group will survive one year is 099 Such a person wishes to buy a 75000 one year term life insurance policy This means that if the person dies in the next year the company will pay 75000 Let C denote how much the insurance company charges for such a policy If X denotes the net pro t to the company from selling the policy what is the probability function of X a fXx 099x 001 x 75000 for 0 lt x lt 1 b pXX 8gtlt gt 099 if x G 001 if x 75000 0 otherwise C pXX 8gtlt gt 099 if x 039 001 if x C 75000 0 otherwise National University of Singapore Page 1 GEM2900 20142015 Semester Assignment 2 Exercise 4 For Exercise 3 the value that C should be for the expected net pro t to be zero is Round your answer to two decimal places For example 300 312 010 Exercise 5 Suppose 10 people buy such a policy as mentioned in Exercise 3 Using the law of rare events or otherwise what is the approximate probability that exactly 2 of them die in the next year Pick the option closest to the answer a 01 b 03 C 05 d 07 e 09 Exercise 5 In 30 independent ips of a fair coin the expected number of runs in the sequence is Round your answer to two decimal places For example 300 312 010 Exercise 7 Investigators need to determine which of 500 adults have a certain medical condition that a ects 2 of the population A blood sample is taken from each of the individuals Assume that the 500 adults are a random sample from the population at large Instead of testing all 500 blood samples investigators group the samples into 50 groups of 10 each mix a little of the blood from each of the 10 samples in each group and test each of the 50 mixtures What is the probability that any such mixture will contain the blood of at least one diseased person and hence test positive Pick the option closest to the answer a 01 b 03 C 05 d 07 e 09 Exercise 8 In the 50 mixtures of blood as mentioned in Exercise 7 the expected number of mixtures that will test positive is Round your answer to two decimal places For example 300 312 010 National University of Singapore Page 2

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