Question: [Discrete Random Variables] According to an agreement between a smartphone producer and a retail company, the former delivers a large batch of smartphones of

[Discrete Random Variables] According to an agreement between a smartphone producer and a retail company, the former delivers a large batch of smartphones of some given model. The retail company applies a quality check by randomly selecting 100 smartphones from the batch, and, if 3 or more of these smartphones are found defected, the entire batch is rejected. Suppose a historical defect rate for this type of smartphones is p = 0.005. Derive (and compute) the probability that the batch is not rejected (a) using an exact approach with the Binomial distribution; (b) using an approximation with the Poisson distribution.

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