Problems: 1. (12 points) For the following scenarios give the following: (a) State which distribution you should use (Hy

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Problems 1 12 Points For The Following Scenarios Give The Following A State Which Distribution You Should Use Hy 1 (302.23 KiB) Viewed 10 times

Problems: 1. (12 points) For the following scenarios give the following: (a) State which distribution you should use (Hypergeometric, Binomial, Negative Binomial, or Poisson). (b) Define the random variable in the question and state the parameter values. (c) Express the probability asked for in the question in terms of the random variable, e.g. P(X = 1), P(X > 5), etc. Do not compute the probability. Notes: • Make sure your definition of the random variable aligns with the question being asked. • You do NOT need to find the value of the probability. • Hypergeometric Distribution Parameters: N, n, k, N-k • Binomial Distribution Parameters: n, p • Negative Binomial Distribution Parameters: k, p • Poisson Distribution Parameters: A, t, or A t Scenarios: (a) A garden contains 15 plants. 10 are tomato and 5 are eggplant. A person selects 8 plants randomly. What is the probability they selected exactly 5 tomato plants? (b) The number of times a server crashes has an average of 3.0 per month. What is the probability that there are fewer than 40 crashes in a year? (c) The probability a person is allergic to cats is 0.15. 30 people are selected randomly. What is the probability that 22 or more of them are allergic to cats? (d) An engineer is going to test components until they find 5 that work. The probability that a component works is .93. Assume each component is independent. What is the probability that the engineer has to test 8 or fewer components to find 5 that work?