A quality engineer samples 100 steel rods made on mill A and 150 rods made on mill B. Of the rods from mill A, 88 meet specifications, and of the rods from mill B, 135 meet specifications.
a. Estimate the proportion of rods from mill A that meet specifications, and find the uncertainty in the estimate.
b. Estimate the proportion of rods from mill B that meet specifications, and find the uncertainty in the estimate.
c. Estimate the difference between the proportions, and find the uncertainty in the estimate.
Let X be the number of rods that meet specifications in the sample from mill A, and let Y be the number of rods that meet specifications in the sample from mill B. Let 
be the probability that a rod from mill A meets specifications and let 
be the probability that a rod from mill B meets specifications. Then X ~ Bin(100,) and Y ~ Bin(150,). The observed value of X is 88 and the observed value of Y is 135.
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