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Stats Professor Exam 2
1. An important bolt is manufactured for use in high speed trains at a plant in Germany. The lengths of the manufactured bolts are normally distributed with a mean of 20.0 cm and a standard deviation of 0.042 cm. Because of variation due to operator error and other more subtle issues, some bolts are made too short and others are too long to be used safely. Bolts that come off the production line shorter than 19.88 cm or longer than 20.12 cm cannot be used. What percentage of bolts will be unusable?
2. International flights allow checked luggage to weigh up to 22 kg without additional charge. However, if you go over, the penalty can be steep. If baggage weights are normally distributed with a mean of 18.8 kg and a standard deviation of 1.9 kg, what percentage of passengers will be forced to pay the penalty or to remove items from their luggage?
3. Measurement error is common especially when the measurements are made by human researchers. If the measurement errors for body fat measurements are normally distributed with an average of 4 percentage points and a standard deviation of 0.53 points, what is the probability that a particular body fat reading taken by a researcher will be in error by at most 3 percent?
6. For young poplar trees aged 18-24 months old, their heights are normally distributed with a mean of 91.44 cm and a standard deviation of 13.1 cm. If samples of 49 young poplar trees are selected at random from the population, would the average heights of those samples be as varied as the individual measurements taken for each tree?