A production process outputs items in lots of 50. Sampling plan exist in which lots are pulled aside periodically and exposed to certain type of inspection. It is usually assumed that the proportion defective is very small. It is important to the company that lots containing defectives be a rare event. The current inspection plan is to periodically sample randomly 10 out of the 50 items in a lot and, if none are defective, to perform no intervention.
a. Suppose in a lot chosen at random, 2 out of 50 are defective. Calculate the probability that at least 1 in the sample of 10 from the lot is defective.
b. Calculate the mean number of defects found out of 10 items sampled.
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