9) Suppose the number of customers arriving each hour at the only checkout counter in a local pharmacy is approximately Poisson distributed with an expected arrival rate of 20 customers per hour. a. Find the probability that exactly 10 customers arrive in a given hour. b. Find the probability that at least five customers arrive in a given hour. c. Find the probability that no more than 25 customers arrive in a given hour. d. Find the probability that between 10 and 30 customers (inclusive) arrive in a given hour.
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Given that the expected arrival rate is 20 customers per hour, we can use the Poisson distribution formula: \[ P(X = 10) = \frac{e^{-20} \cdot 20^{10}}{10!} \] \[ P(X = 10) = 0.0058 \] Show more…
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