Consider the defective computer chip example we discussed in class. As part of a quality control process for computer chips, an engineer at a factory randomly samples 212 chips during a week of production to test the current rate of chips with severe defects. She finds that 27 of the chips are defective.
The information above describes the outcome of a single sample. Suppose the true proportion of defective chips at this factory is p=0.1.
(a) Using R or Desmos, calculate the probability of collecting a sample of size n=212 and observing a sample proportion of defective chips of 0.127 or less. That is, calculate
. Round your answer to three decimal places.
(b) Using R or Desmos, calculate the probability of observing a sample proportion of defective chips that is within two standard errors of the true population proportion, p. Round your answer to 3 decimal places.
