Tutorial 1 Questions

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Jan 9, 2024

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University of Toronto Department of Mechanical and Industrial Engineering MIE236: Probability (Fall 2023) Tutorial 1 Problem 1: If ? and ? are two sets then ? ∩ (? ∪ ?) 𝑐 is equal to : A. B B. A C. ∅ D. ? ∪ ? Problem 2: Consider the following Venn diagram, where ?, ? and ? are three sets. Let the number of elements in ? be denoted by 𝑛(?) . which is equal to 90. What is the value of 𝑛(?) + 𝑛(?) + 𝑛(?) − 𝑛(? ∩ ?) − 𝑛(? ∩ ?) − 𝑛(? ∩ ?) + 𝑛(? ∩ ? ∩ Z)? A. a+b+43 B. a+b+63 C. a+b+96 D. a+b+106 Problem 3: In a city, there are 3 major newspapers A, B and C of which at least two are read by 35% of population. A and B are read by 15%. C is read by 45% and that all the three are read by 10%. Then the percentage of people who read the newspaper C alone is A. 20 B. 10 C. 15 D. 25 E. 5

University of Toronto Department of Mechanical and Industrial Engineering MIE236: Probability (Fall 2023) Problem 4: A study of 2007 model automobiles was conducted. In the study the following variables were considered: the Region in which the car was manufactured (Europe, North America, Asia); the Type of automobile (compact, midsize, large), volume of the engine in liters, and the type of Fuel used (regular, premium, 85% Ethanol). The variables Region, Type, volume, and Fuel are, respectively are: A. quantitative, categorical, categorical, quantitative. B. categorical, quantitative, quantitative, categorical. C. categorical, categorical, quantitative, quantitative. D. categorical, categorical, quantitative, categorical. E. Unable to determine without knowing the values of the various variables. Problem 5: The boxplot of the ages (in years) of the employees in a company is shown below. Read the following statements regarding the distribution age of these employees: I. The distribution is skewed to the right. II. The interquartile range is 8 years. III. The median is about 40 years. Which of the above three statements is (are) correct? A. Only III is true. B. Only II and III are true. C. Only I and II are true. D. Only I is true. ! E. Only II is true.

University of Toronto Department of Mechanical and Industrial Engineering MIE236: Probability (Fall 2023) Problem 6: For data on a quantitative variable, which of the following is true? A. If the distribution is symmetric, then the range is an appropriate measure of the center. B. If the distribution is symmetric, then the standard deviation is an appropriate measure of the center. C. If the distribution is skewed, then the mean is an appropriate measure of the center. D. If the distribution is skewed, then the median is an appropriate measure of the center. E. If the distribution is skewed, then the standard deviation is an appropriate measure of the spread. Problem 7: Of the following measures: mean, median, IQR (inter-quartile range), and standard deviation, which measures are resistant to outliers? A. Mean and median B. Median and IQR C. Mean and standard deviation D. Median and standard deviation E. None of the above Problem 8: A magazine commissioned a study to find the number of days in the standard high- school year in different countries and provinces. A boxplot is shown below. Which is the correct statement to compare the mean and the median? A. They should be similar. B. Mean is larger than the median. C. Can't decide based on this information. D. Median is larger than the mean.

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