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Part 1. (6 points) Identify the distribution For each random variable: State the distribution that will best model random variable. Choose from the common distributions: Uniform, Exponential or Normal distribution. Explain your reasoning. State the parameter values that describe the distribution. Give the probability density function. a. b. c. Random Variable 1 A statistics student has a part time job as a coffee shop barista, she realizes the time between customer orders is a random variable. During an eight-hour shift, she measures time between successive customer order and finds that the time between customer orders is on average 30 seconds. Furthermore, she discovers times are more likely to be close to O, and less likely as they get further away from o. Random Variable 2. In a board game, individuals must attempt to guess a phrase based on clues from their teammate. If they successfully guess the phrase before a buzzer sounds, their teammate may give clues for another phrase. Each correctly guessed phrase, before the buzzer sounds, gives them a point in the game. The buzzer is set to a random time increment anywhere between 30 and 90 seconds. Consider time until the buzzer sounds a random variable where any time between 30 and 90 has an equal likelihood. Random Variable 3 An industrial process yields a large number of steel cylinders. The length of the cylinder is a random variable with an average of 3.25 inches and a standard deviation of 0.003 inches. The distribution of inder lengths is symmetrical, where lengths are more likely to be close to the mean rather than further away from the mean.

Answer 1