The range to an electric car is the amount kilometers the car can drive when the battery is full until it is empty. Anna owns an electric car which has a range that is normal distributed with expected 305 km, and standard deviation 23 km. Anna always starts a car ride with a full battery. a) i: Anna drives from point A to point C, a distance 301 km. What is the probability that she has enough range to drive the distance without charging during the trip? ii: What is the probability for Anne to run out of battery during between point A to point B her trip to point C? The distance between point A and point B is 281 km. iii: At another trip Anne is going to drive from point A to point D. She plans to stop and charge the battery at point B (after 281 km), and from there drive all the way to point D without stop. The distance from point B to point D is 276 km. What is the probability for that she can complete the trip as planned without running out of battery between Point A and point B, or point B and point D. Assume that the two distances are independent.

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Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!