Suppose that Medtronic has a heart arrhythmia monitoring sys

Suppose that Medtronic has a heart arrhythmia monitoring system that fails with probability 10^-6. Suppose that the US has approximately 3 million people with Medtronic monitors implanted. Use the Poisson approximation to the Binomial to approximate the probability that the number of people in the US whose Medtronic arrhythmia monitoring system fails is greater than 2.

Solution

X = no of people in the US whose Medtronic Arrhythmia monitoring system fails

X follows a Poisson with p = 10^-6. n = 3 million

Hence X has a Poisson with parameter np = 3,000,000x10^-6 = 3

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Required probability = P(X>2)

= 1- cum prob for Poisson <=2

= 0.5768