1. The time, in hours, that a copying machine may work without breaking down is a normally distributed random variable with mean 549 and standard devia- tion 68. Find the probability that the machine will work for at least 500 hours without breaking down.
2. The yield, in tons of ore per day, at a given coal mine is approximately nor- mally distributed with mean 785 tons and standard deviation 60. Find the probability that at least 800 tons of ore will be mined on a given day. Find the proportion of working days in which anywhere from 750 to 850 tons is mined. Find the probability that on a given day, the yield will be below 665 tons.
3. Scores on a management aptitude examination are believed to be normally dis- tributed with mean 650 (out of a total of 800 possible points) and standard deviation 50. What is the probability that a randomly chosen manager will achieve a score above 700? What is the probability that the score will be below 750?