Random sampling from a large lot of manufactured items yields a number of defective items X with an approximate binomial distribution with p being the true proportion of defectives in the lot. A sampling plan consists of specifying the number, n, of items to be sampled and an acceptance number $a$. After n items are inspected, the lot is accepted if X \leq a and is rejected if X > a. A. For n = 100 and a = 20 calculate the probability of accepting the lot for values of p equal to 0, 0.1, 0.3, 0.5 and 0.9 and 1. Write the six acceptance probabilities, separated by commas.
B. Graph the probability of lot acceptance as a function of p. This is called an operating characteristic curve. They key is to store your lists of ps and your list of probabilities as vectors in R, and then to use these as the X and Y axes in a geom_line() plot.