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Question 1 [Marks: 25) 9.1.1 The following contingency table gives the results of a sample survey of South African male and female respondents with regard to their regular mode of transport: Regular Mode of Transport Car Bus Taxi Total No. of Females 65 85 40 190 No. of Males 60 90 60 210 Total 125 175 100 400 Q.1.1.1 What is the probability of randomly selecting a female respon given that they travel by bus? Q.1.12 What is the probability of randomly selecting a respondent who is 141 male or travels by taxi? Q.1.13 What is the probability of random indent who is not (3) male? Q.1.2 Events A and B are such that P(A) = 0.20 and P(A U B) = 0.55. Given that A (5) and # are independent and non-mutually exclusive, determine P(B). Give your final answer as a percentage to two decimal places. Q.1.3 Briefly discuss each of the five basic properties that apply to every probability. (10) Question 2 [Marks: 20) Q.2.1 It has been found that 1 out of every 4 cars that go through an NI tollgate are from Limpopo. If we randomly select a sample of 11 cars that go through the tollgate, what is the probability that: q.1.1.1 No more than two of the cars are from Limpopo? interpret your answer. 9-212 More than three of the cars are from Limpopo? Interpret your 150 answer. Q.2.2 The marks obtained on a Maths Olympiad test are normally distributed, with an average score (u) of 87 and a standard deviation jo) of 9.75. What is the probability that a randomly selected person will: 9.2.21 Obtain a score between #8 and 90? Interpret your answer Q.2.2 2 Obtain a score between 84 and 91? Interpret your andwer Question 3 [Marks: 15) 0-1.1 Give a definition of what is meant by the term "sampling distribution of the sample means". q.3.2 Define the term "sampling error". (2) q.1.5 Glass Houses Pty has found that 20% of its customers live in the Cape Town area. A sample of 155 customers is randomly selected. Assuming normal distribution Q-3.3.1 Determine the standard error for this sample q.1.1.2 What is the probability that more than 24%% of the customers in the sample live in the Cape Town area? interpret your answer. END OF PAPER