### BUS105: Statistics

Question 1

• Dr. Tan has taught BUS105 for many years, and he knows that around 75% of students will read the study guide. Among those who read the study guide, 87% will pass the course. Among students who did not read the study guide, 65% will pass the course.

a) Identify the probability that a student will pass BUS105.
b) Raymond took BUS105 last semester, and he passed BUS105. What is the probability that he had read the study guide?

• Statistics show that the distribution of monthly rent for a 4-room HDB flat has a mean of \$2,530 and a standard deviation of \$240.

a) Assume that the distribution of monthly rent for a 4-room HDB flat follows a normal distribution, what is the probability of renting a flat at a price cheaper than \$2,000?
b) In fact, the distribution of monthly rent for a 4-room HDB flat is positively skewed. What is the probability of finding the mean rent of a sample of 35 units of 4-room HDB flats more than \$2,600?

Question 2

Table 1 shows the median gross monthly income from work (including employer CPF contributions) of full-time employed residents for 2011-2021.

Table 2-1: Median gross monthly income from work of full-time employed residents