Match each distribution, and explain why, to each of random variable scenarios p
ID: 3201025 • Letter: M
Question
Match each distribution, and explain why, to each of random variable scenarios provided below. Each option can only be used once. Binomial Distribution Poisson Distribution Normal Distribution Exponential Distribution Gamma Distribution Uniform Distribution A manufacturer of copper wire knows the number of flaws on a certain type of wire has a discrete probability distribution with an average of 1.5 flaws per millimeter. What type of distribution should be used to model this random variable Consider X to be the time between speeding vehicles on a roadway. The distribution of X is positively skewed and described by one parameter. The mean of X is 16 minutes. What type of distribution should be used to model this random variable? The daily amount of coffee dispensed by a machine in a hotel lobby is a random variable between 7 and 10 liters. The distribution in liters of coffee dispensed is continuous and symmetric. The amount of coffee dispensed an average is 8.5 liters and all amount between 7 and 10 liters have an equal likelihood of occurring. What type of distribution should be used to model this random variable? The time between two stops on a high speed commuter train is a random variable with a mean of 28 minutes and a standard deviation of 2 minutes. The distribution of times is symmetric where commuting times further away from the mean become increasingly less likely. What type of distribution can be used to model the commuting times on the train? A safety engineer claims the probability of an individual worker wearing a safety helmet while eating their lunch on the job site is 40%. Suppose 20 workers are selected at random, X is the random variable that models the number of workers wearing a helmet during their lunch break. It is assumed that whether a worker is wearing their helmet is independent between workers that are selected. What type of distribution can be used to model the probability of X?Explanation / Answer
a) Poisson Distribution ( Since its mean is known and the variable of interest is flaws (defectives) and it is discrete)
b) Exponential distribution ( Since the data is skewed)
c) Normal distribution ( Since the data is symmetric & continuous)
d) Normal distribution ( Since the data is symmetric & continuous)
e) Binomial Distribution (Since the data is independent & have 2 possible outcomes)