Problem Set 1 - Probability Group No. and Names Problem Set 1 1. Refer to the contingency table below. {30 marks) Maj or None Beginner Intermediate Expert STEM 8 7 1 1 39 ABM 1 1 4 1 1 3 9 HUMS 9 1 1 25 19 a. Find the probability that a customer is an ABM student or a beginner in computer. b. Find the probability that a customer is HUMS student provided someone that do not know in computer. c. What is the probability that a customer is not a STEM student and intermmediate in computer? d. Find the probability that two customers will be chosen for scholarships provided they are STEM and experts in computer. e. Create a pie graph for the different majors. f. Create a bar graph for the different type of computer abilities. 2. A Harris Interactive poll conducted in Fall, 2002 {AI) via a national telephone survey of adults asked, "Do you think adults should be allowed to legally use marijuana for medical purposes if their doctor prescribes it, or do you think that marijuana should remain illegal even for medical purposes?" The results showed that 80 percent of respondents answered "Yes" to the above question. Assuming 80 percent of Americans would say "Yes" to the above question, do the following. (20 marks) a. Find the probability when eight Americans are chosen at random that five or more said "Yes". b. Find the probability when eight Americans are chosen at random that between ve and six inclusive said llYesll c. Create a graph of the distribution. 3. In a study by Thomas et al. (A14) the Poisson distribution was used to model the number of patients per month referred to an oncologist. The researchers use a rate of 15.8 patients per month that are referred to the oncologist. (20 marks) a. Calculate the probability that in a month between 5 and 13 inclusive are referred to an oncologist. b. Calculate the probability that in a month less than 9 are referred to an oncologist. c. Create a graph of the cumulative distribution. 4. A mall supervisor has found that mall sellers, on average, complete a certain task in 10 minutes. If the times required to complete the task are approximately normally distributed with a standard deviation of 3 minutes. (20 marks) a. Find the proportion of mall sellers completing the task in less than 2.6 minutes. b. Find the proportion of mall sellers requiring more than 3.5 minutes to complete the task' c. Find the probability that a mall seller who has just been assigned the task will complete it within 2 minutes. d. Find the probability that a mall seller can complete the task between 2.1 and 13.8 minutes