1. Color blindness appears in 2% of the people in a certain population. How large must a random sample be in order to be 99% certain that a color-blind person is included in the sample?
2. A shirt manufacturer knows that, on the average, 2% of his product will not meet quality speci?cations. Find the greatest number of shirts constituting a lot that will have, with probability 0.95, fewer than ?ve defectives.
3. A random sample of size 100 is taken from a population with mean 1 and variance 0.04. Find the probability that the sample mean is between 0.99 and 1.
4. The lifetime X (in hours) of a certain electrical component has the pdf f(x) = (1/3)e-(1/3)x,x > 0. If a random sample of 36 is taken from these components, ?nd P(X 2).
5. A drug manufacturer receives a shipment of 10,000 calibrated "eyedroppers" for administer- ing the Sabin poliovirus vaccine. If the calibration mark is missing on 500 droppers, which are scattered randomly throughout the shipment, what is the probability that, at most, two defective droppers will be detected in a random sample of 125?