ECO220_Test3_Fall2018.pdf - ECO220Y5Y Quantitative Methods in Economics Test 3 \u2013 Topic 3 Time allowed 1 hour Answer all questions Calculators may be

# ECO220_Test3_Fall2018.pdf - ECO220Y5Y Quantitative Methods...

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ECO220Y5Y: Quantitative Methods in Economics Test 3 – Topic 3 Time allowed 1 hour. Answer all questions. Calculators may be used. No Outside Materials – Cheat Sheet included with test Question 1 In the 2017 season Toronto FC (TFC) were a great team and Giovinco scored 25 goals in a stretch of 25 games. Based on the 2017 season answer the following: (assume Giovinco will play the first 25 games of next season) 1. What is the probability he will score six or more goals in his first four games of the next season? 2. What is the probability he opens the first half of his first game in the next season with a brace (2 goals)? 3. Assume all games last exactly 90 minutes. What is the probability fans will have to wait 270 minutes or longer into the first 25 games of next season until Giovinco scores his first goal? 4. Assuming Giovinco scores in a game then TFC win. If he does not score they lose. What is the probability they will win at least 80% of the 25 games he plays next season? Question 2 In each part assume the following and solve: 1. Assume X F 10 , 5 . Solve for P ( X 3 . 3). 2. Assume X F 1 , 23 . Solve for P ( X 6 . 25). 3. Assume X F 1 , 1 . Solve for P ( X 1). 4. Assume X t 25 . Solve for P ( - 2 . 060 X  - 1 . 485). page 1 of 2 ECO220Y November 30, 2018 Question 3 Consider the following binomial distribution: 3.125 3.125 15.63 15.63 31.25 31.25 31.25 15.63 3.125 0 0 10 10 20 20 30 30 Percent Percent 0 1 1 2 2 3 3 4 4 5 5 pdf pdf Binomial Density (PDF) Binomial Density (PDF) 1. Solve for the mean and standard deviation of the binomial distribution 2. Solve for P ( X > 3) in the binomial distribution 3. Solve for the mean and standard deviation of ONE Bernoulli trial from this binomial distribution 4. Now assume there are 200 of these Bernoulli trials in the binomial. Use an approximation to the normal to solve for P ( X < 30) (use your p from part 3) Question 4 Last summer the chance of failing ECO220 was 8%. You decide to put together a random sample of 35 friends from ECO220 from the summer and use this to solve the following: 1. What is the mean and variance of the sampling distribution? 2. What is the probability that in your sample of friends between 2 and 4 of them failed? (hint: use sampling distribution) 3. What is the probability that in your sample more than 32 of them passed? (hint: use sampling distribution) page 2 of 2 Quantitative Methods in Economics ECO220Y5Y – Cheat Sheet Formulas & Statistical Tables for Economists page 1 of 16 