A person with a cough is a persona non grata on airplanes, elevators, or at the theater. In theaters especially, the irritation level rises with each muffled explosion. According to Dr. Brian Carlin, a Pittsburgh pulmonologist, in any large audience you'll hear about 15 coughs per minute. (a) Let r = number of coughs in a given time interval. Explain why the Poisson distribution would be a good choice for the probability distribution of r. Coughs are a common occurrence. It is reasonable to assume the events are dependent. Coughs are a rare occurrence. It is reasonable to assume the events are dependent.     Coughs are a common occurrence. It is reasonable to assume the events are independent. Coughs are a rare occurrence. It is reasonable to assume the events are independent. (b) Find the probability of twelve or fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.) (c) Find the probability of at least nine coughs (in a large auditorium) in a 32-second period. (Use 4 decimal places.)

A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour.   It takes an average of 2 minutes to answer a question.   It is assumed that arrivals are Poisson and answer times are exponentially distributed.   What is the arrival rate? (Include the units.) What is the service rate? (Include the units.) Find the probability that the employee is idle.

Susan collects data on three random variables, X, Y, and Z. She plots histograms of her data to help her decide which probability distribution is likely to be most suitable for each of these three random variables. (a) Based on the histogram below, which of the following distributions; Bernoulli; discrete uniform; continuous uniform; normal or exponential distribution is the most likely distribution for the random variable X? Abuanbaug 250 Frequency 200 150 100 (b) Based on the histogram below, which of the following distributions; Bernoulli; discrete uniform; continuous uniform or exponential distribution is the most likely distribution for the random variable Y? 120- 100 Histogram of X 20 Histogram of Y

A certain kind of sheet metal has, on average, 4 defects per 20 square feet.Assuming a Poisson distribution, find the probability that a 28 square foot metal sheet has at least 7 defects. Round your answer to three decimal places.