By: ECON 310 Economic and Business Statistics Module 1 Assignment 1. The number of times a particular event occurred in the past is divided by the total number of occurrences. What is this approach to probability called? (2 marks) 2. Is it true that if there is absolutely no chance that a corporation will assume partnership with a merging company, the probability assigned to this event is -1.00? If not true, what is the probability? (2 marks) 3. According to a Statistics Canada report on physical activities of Canadians 12 years of age and over, 50.42% of the population is male. Of these 50.42%, 16.51% are engaged in physical activities regularly. What is the probability of randomly selecting a Canadian who is both male and physically active? (2 marks) 4. Ace construction Company has agreed to offer a variety of exterior designs for new homes being built in a Western Canadian subdivision. 5 exterior designs are offered to potential home buyers. The builder has standardized 3 interior plans that can be incorporated with any of the 5 exterior designs. How many different ways can the exterior and interior plans be offered to potential home buyers? (10 marks) 5. The Daily, a Statistics Canada publication reported that 5% of college and bachelor degree students default on their student loans within two years of graduation. Suppose a random sample of nine college and bachelor degree students is taken. (15 marks) a) What is the probability that exactly 2 students of the selected group will default on their loans? b) What is the probability that at least 3 students will default? c) What is the probability that none of the 9 students will default? d) What are the average and standard deviation of the number of students from the group of 9 who will default on their loans? 6. The manager of a Vancouver nightclub has observed that the number of male customers who visit the club follows a Poisson distribution with a mean of 30 per day, and the number of female customers who visit the club follows a Poisson distribution with a mean of 20 per day. The entrance ticket is $20 per male and $10 per female. (10 marks) a) Find the probability that 10 males will visit the club on a randomly selected day. b) If the number of males and female visitors are mutually independent, find the mean and the standard deviation of the club earnings through entrance ticket earnings. 7. Suppose 1.5% of the plastic spacers produced by a Corson high-speed mould injection machine are defective. For a random sample of 200 spacers, find the probability that: (10 marks) a) None of the spacers are defective By: ECON 310 Economic and Business Statistics b) 3 or more of the spacers are defective 8. A normal population has a mean of 20.0 and a standard deviation of 4.0. (20 marks) a) Compute the z values associated with 18.0, 20.0 and 25.0? b) What proportion of the population is between 20.0 and 25.0? c) What proportion of the population is less than 18.0? 9. A recent ICBC study has shown that 40% of the high-speed chases involving automobiles result in a minor or major accident. During a month in which 50 high-speed chases occur, what is the probability that 25 or more will result in a minor or major accident? (15 marks) 10. Mensa is an organization whose membership requires an IQ in the top 2% of the general population. 500 people are chosen randomly. (14 marks) a) What is the probability that no more than 4 of them will qualify for membership to Mensa? b) What is the probability that at least 8 of them will qualify for membership to Mensa