1. There're four inspectors who are scheduled to work 7:00 AM - 3:00 PM shift every day at the nearby airport. Each day there is the 0.15 chance that each inspector will unexpectedly not report for work. If there ever are less than three inspectors on duty, the security checkpoint should be shut down till a substitute inspector(s) can be brought in to work the remainder of the shift. Let Y be the number of inspectors that show up for 700 AM - 300 PM shift on given day. Find out the probability that the security checkpoint will be shut down tomorrow?
2. There're 30 identical items in the delivery box. For the box to pass inspection, at least 20 of those items must be in good condition. If the inexperienced quality inspector find out randomly whether or not an item is in good condition, find out the probability that the box will pass inspection?
3. Past data point out that the variance of measurements made on sheet metal stampings by experienced quality-control inspectors is 0.025 square inch. Such measurements made by the inexperienced inspector could have too large the variance (perhaps because of inability to read instruments properly) or too small the variance (perhaps because unusually high or low measurements are discarded). If the new inspector measures 101 stampings with variance of 0.13 square inch, test at the 0.05 level of significance whether inspector is making satisfactory measurements. Suppose normality.