Question

3. (a) Consider the population of all families with two teenagers and a maid. Let G denote a girl, B denote a boy and M denote a maid. Assume that a teenager is equally likely to be a girl or a boy. We are interested in the timing sequence of the teenagers and the maid (in the same family) going to bed on a Saturday night. Let BMB represents one teenage boy goes to bed first, the maid goes to bed next and another teenage boy goes to bed last. Here we are not concerned with the order (younger vs elder) of the boys. (i) Write down all the possible timing sequences of going to bed on a Saturday night for a family with two teenagers and a maid. (ii) A family is selected at random from the population. Assume that all Find the probability that the maid is the first one to go to bed on a Given that the family has at least a teenage boy, find the probability (7 Marks) timing sequences are equally probable Saturday night. that the last one to go to bed on a Saturday night is a boy (b) The number of fallen trees in a district can be modelled by the Poisson distribution. On average, there is 1 fallen tree per month. What is the probability that there are at most 2 fallen trees in a month? Today is 28 April and so far we have had 1 fallen tree in April. What is the probability that there are at most 2 fallen trees in the month of April? Give your answers correct to 4 decimal places (9 Marks) (c) A property agent has obtained a random sample of 31 recent rental transactions in the city area. From the sample it was found that the RSF (rental per square foot) had a mean of $4.70 and a standard deviation of $1.10 On the other hand, there were reports that indicate properties in the Sentosa Island fetched an average RSF of $4.30. Based on the sample obtained by the property agent, can he conclude, at the 5% level of significance, that properties in the city area enjoy higher rentals than those in Sentosa Island? For what range of level of significance a will the conclusion be reversed? 9 Marks)

Answer 1

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