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 Math Central Quandaries & Queries
 Question from Venni: The Medassist Pharmaceutical Company receives large shipments of aspirin tablets and uses this acceptance sampling plan: Randomly select and test 24 tablets, then accept the whole batch if there is only one or none that doesn’t meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted?

Hi Venni,

I think you are expected to use the Binomial Distribution. That is you have an experiment (select a tablet and test it) that you repeat $n$ times $(n = 24),$ the repetitions are independent. I am going to say that success on performing the experiment is finding a defective tablet. The rate of defective pills is 4% and you need to then assume that the probability of success on each repetition of the experiment is given by $p = 0.04.$ Let $X$ be the random variable that counts the number of successes in the $n$ repetitions of the experiment. The expression you need is that for each integer $r$ between 0 and 24

$P(X = r) = {n \choose r} p^r (1-p)^{n-r}$

Where $P(X=r)$ is the probability that X (the number of successes) is $r.$

Penny