Topic3_ProbabilityDistributions_TestReview.pdf - ECO220Y5Y Quantitative Methods in Economics Topic Three \u2013 Probability Distributions Test Review

# Topic3_ProbabilityDistributions_TestReview.pdf - ECO220Y5Y...

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ECO220Y5Y: Quantitative Methods in Economics Topic Three – Probability Distributions Test Review Questions Tutorials – Fall/Winter 2017/18 The variable income measures the average annual income five years after graduating of university students who get a first class mark in their ECO220 course. The variable is normally distributed and has a mean of \$60,000 and a standard deviation of \$5,000. 1. Assuming you get a A in ECO220, what is the probability you will earn an annual average annual income five years after graduating of less than \$50,000? 2. Assuming you get a A in ECO220, what is the probability you will earn an annual average annual income five years after graduating of more than \$60,000? Tutorials – Fall/Winter 2018/19 Suppose the probability is 0.5 that the value of the \$US will rise against the \$CAN over any given week. You also know that the outcomes of the week on week changes are independent of one another. 1. What is the probability that the value of the \$US will rise against the \$CAN in a majority of the weeks over a period of 7 weeks? 2. What is the probability that the value of the \$US will rise against the \$CAN in each of the 7 weeks? 3. What is the probability that the value of the \$US will rise against the \$CAN more than once in the 7 weeks? Tutorials – Summer 2019 A lecturer found that time spent by students on an exercise sheet follows a normal distribution with mean 60 minutes and standard deviation 18 minutes. 1. The probability is 0.9 that a randomly chosen student spends more than how many minutes on this exercise sheet? 2. The probability is 0.8 that a randomly chosen student spends less than how many minutes on this exercise sheet? 3. Two students are chosen at random. What is the probability that at least one of them spends at least 75 minutes on the exercise sheet? page 1 of 7
ECO220Y November 15, 2019 Test – Fall/Winter 2017/18 – Question 3 After surveying students at UTM it is determined that 2% of all students are dissatisfied with the availability of food options on campus. A random sample of 10 students was then taken: 1. What is the probability that at least 2 students in the sample were dissatisfied with the food options on campus? 2. What is the probability that the number of students in the sample who were dissatisfied with food options was between 1 and 3? 3. Suppose a sample of 600 students was taken instead, use an approximation to the binomial distribution to estimate the probability 6 or fewer of them were dissatisfied with food options. Test – Fall/Winter 2017/18 – Question 4 A random variable X measures student grades (%) from a recent statistics test which follows a normal distribution with mean 65 and variance 225 ie. X N (65 , 225) 1. What is the minimum score needed for a student to be amongst the highest 16% of the class? 2. What is the probability a randomly selected student has failed?

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