An inspector monitors large truckloads of potatoes to determine the proportion p of potatoes with major defects before the potatoes are used to make chips. They intend to compute a 95% confidence interval for p. To do so , they select a simple random sample of 50 potatoes from a truckload of more than 2000 potatoes. Suppose that only 2 of the 50 potatoes sampled are found to have major defects. Determine if the conditions for inference using a confidence interval are met.