BUS105 STATISTICS

Question 1 Table 1 shows the median gross monthly income from work (including employer CPF contributions) of full-time employed residents for 2011-2021. Table 1-1: Median gross monthly income from work of full-time employed residents Median gross monthly income ($) 2011 3.249 2012 3,480 2013 3,705 2014 3,770 2015 3,949 2016 4,056 2017 4,232 2018 1,437 2019 4,563 2020 4.534 2021 1,680 Source: Ministry of Manpower, Singapore. (a) Calculate the average annual change in median gross monthly income for the period 2011-2016 and 2016-2021, respectively. (4 marks) (b) Calculate the cumulative change in median gross monthly income for the period 2011-2016 and 2016-2021, respectively. (4 marks) (c) Discuss your observations on the income trends in the past decade, based on your answers to part (a) and (b), as well as some graphic representation. (8 marks) (d) In November 2021, the government accepted the progressive wage proposal for the security sector which sets the monthly gross salaries of entry-level security officers to a minimum of S$3,530 by 2028. The current minimum monthly gross salary of entry-level security officers is $1,400 in 2021. Compare the expected change of minimum monthly salary of entry-level security officers to the income trends discussed above. Comment on the progressive wage model (hint: the pros and concerns related to the progressive model). (9 marks)Question 2 (a) Dr. Tan has taught BUSIDS many years. and he knows that around "5% of' students will read the study guide. Among those who read the study guide, RT% will pass the course. Among students who did not read the study guide, 65% will pass the course. (i) Identify the probability that a student will pass BUS [05. (5 marks) (ii) Raymond took BUSIDS last semester, and he passed BUS [05. What is the probability that he had read the study guide? (7 marks) (b) Statistics show that the distribution of'monthly rent for a 4room HDB flat has a mean of52,530 and a standard deviation of'5240. (i) Assume that the distribution of' monthly rent for a 4room HDB flat follows a normal distribution, what is the probability of renting a at at a price cheaper than 52.000? (5 marks) (ii) In fact, the distribution of monthly rent for a 4room HDB Flat is positively skewed. What is the probability of nding the mean rent of'a sample of 35 units of4room HDB at more than $2,600? (8 marks)