Every day, patients arrive at the dentist’s office. If the Poisson distribution were applied to this process: a.) What would be an appropriate random variable? What would be the exponential-distribution counterpart to the random variable? b.)If the random discrete variable is Poisson distributed with λ = 10 patients per hour, and the corresponding exponential distribution has x = minutes until the next arrival, identify the mean of x and determine the following: 1. P(x less than or equal to 6) 2. P(x greater than or equal to 7.5)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Every day, patients arrive at the dentist’s office. If the Poisson distribution were applied to this process:
a.) What would be an appropriate random variable? What would be the exponential-distribution counterpart to the random variable?
b.)If the random discrete variable is Poisson distributed with λ = 10 patients per hour, and the corresponding exponential distribution has x = minutes until the next arrival, identify the mean of x and determine the following:
1. P(x less than or equal to 6) 2. P(x greater than or equal to 7.5)
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