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Problem 2. (15 points). Engineer Nick's sources steel rods for rebar from your even shadier sister-inlaw's company, Fabricator Nicole. In the last shipment of 1000 rods, each rod was supposed to have a length of 5 meters. When you measure them, you nd that the rods actually have a mean length of 5.1 meters, with a standard deviation of 0.2 meters, following a normal distribution. Longer rods are annoying, but salvageahle (you can cut them to the right length), but rods which are too shirt are unusable. (a) (5) Approximately how many rods are 5 meters or longer? (b) (5) What is the 90th percentile length for these rods? (0) (5) You complain that too many of the rods are unusable. A new shipment is ordered, and you are promised that the standard deviation will be reduced, so that 98% of the new batch of rods will satisfy the minimum length of 5 meters. If this promise is upheld exactly, what was the standard deviation in the new batch