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Module/Week 6 Homework: Probabilities and Statistics MGMT 5260: Decision-Making Techniques for Managers Please create a single Excel file with each problem on a separate worksheet tab. Problem 1 A fair coin was tossed 3 times. Calculate the probabilities of the following 5 events. a. Three heads were observed b. Two heads were observes c. One head were observed d. At least two heads were observed e. No more than two tails were observed Problem 2 11% of a city's population are illegal emigrants. Two random people were selected. What is the probability that: a. Both are legal emigrants. b. Only one is a legal emigrant. c. Both are illegal emigrants. Problem 3 The following table shows frequency of iPads sold per day at a local electronie store in January of the current year. During that month, there was never a day in which more than 5 iPads were sold. Problem 3 The following table shows frequency of iPads sold per day at a local electronic store in January of the current year. During that month, there was never a day in which more than 5 iPads were sold. a. Determine the mean number of iPads sold per day in January. b. What is the probability that exactly 4 iPads will be sold in a randomly selected day? c. What is the probability that 1 or 3 iPads will be sold in a randomly selected day? d. What is the probability that no more than 2 iPads will be sold in a randomly selected day? e. What is the probability that at least 3 iPads will be sold in a randomly selected day? Problem 4 A variable Z is normally distributed with =54 and =12.3. Find the following probabilities: a. P(4054) d. P(Z57.3) Problem 5 Using Excel's standard functions: a. Calculate the mean, variance and standard deviation of the students' grades presented below. b. Use the descriptive statistics tool and calculate various statistical measures. Problem 6 The life of an electronic transistor is normally distributed with a mean of 500 hours and a standard deviation of 80 hours. Determine the probability that a. A transistor will last for more than 400 hours? b. A transistor will last for less than 350 hours? c. A transistor will last exactly 501 hours? Problem 7 The weight of bags of fertilizer is normally distributed with a mean of 50 pounds and standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh: a. Between 45 and 55 pounds? b. At least 56 pounds? c. At most 49 pound? Problem 8 The amount of time devoted to studying each week by students who achieve grade A in the course is normally distributed with mean of 7.5 hours and standard deviation of 2.1 hours. Find the probability that an A student study time per week is a. between 7 and 9 hours? b. less than 5 hours? c. exactly 6 hours