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Poisson distributions – Statistics

Can you help me understand this Statistics question?

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Handwritten or typed is fine, as long as it is legible….. we were given these practice problems and I’m struggling with how to approach them and how to answer them properly. Thanks!

2) The probability of a defective pacemaker from a manufacturer is 0.5%. Assuming that you are a physician with 300 patients that have pacemakers, what is the probability that all three of the patients with pacemakers you will see tomorrow will all have defective pacemakers?

3) You could also calculate the probabilities in question 3 using a binomial expansion, but it is a more tedious calculation. Use a binomial expansion to calculate the probability that 3 out of your 300 patients have a defective pacemaker. The answer should be the same as what you discovered in question 2.

4) Imagine that a small hospital ER has an average of 20 admissions on Saturday nights. If you were a doctor working overtime on such a Saturday night, what is the chance you’d have a quiet night (defined as 5 or fewer admissions) to catch up on some much-needed sleep?

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