A company has installed 3288 flow meters throughout an extensive sewer system. Unknown to the company, 592 of these meters are operating outside acceptable tolerance limits, whereas the other 2696 meters are operating satisfactorily. The company decides to estimate the unknown proportion p of the meters that are operating outside acceptable tolerance limits based on the inspection of a random sample of 20 meters.
(a) What is the probability that the company's estimate of p will be within 0.1 of the correct value?
(b) Suppose that 2012 of the meters are easily accessible, whereas the other 1276 meters are not easily accessible. In addition, suppose that only 184 of the easily accessible meters are operating outside acceptable tolerance limits. If the company's sample of 20 meters is biased due to the fact that the meters were randomly chosen from the subset of easily accessible meters, what is the probability that the company's estimate of p will be within 0.1 of the correct value?