Question

Consider a shipment of 1000 items into a factory. Suppose the factory can tolerate about $5 \%$ defective items. Let $X$ be the number of defective items in a sample without replacement of size $n=10$. Suppose the factory returns the shipment if $X \geq 2$. (a) Obtain the probability that the factory returns a shipment of items which has $5 \%$ defective items. (b) Suppose the shipment has $10 \%$ defective items. Obtain the probability that the factory returns such a shipment. (c) Obtain approximations to the probabilities in parts (a) and (b) using appropriate binomial distributions.

          Consider a shipment of 1000 items into a factory. Suppose the factory can tolerate about $5 \%$ defective items. Let $X$ be the number of defective items in a sample without replacement of size $n=10$. Suppose the factory returns the shipment if $X \geq 2$.
(a) Obtain the probability that the factory returns a shipment of items which has $5 \%$ defective items.
(b) Suppose the shipment has $10 \%$ defective items. Obtain the probability that the factory returns such a shipment.
(c) Obtain approximations to the probabilities in parts (a) and (b) using appropriate binomial distributions.

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