A commuter must pass through five traffic lights on her way to work and has to stop at each one that is red. She estimates the probability model for the number of red lights she hits in one day. Based on this model, she expects to hit 2.57 red lights each day, and the standard deviation is 1.36 red lights. Suppose that this commuter has a five-day work week. Complete parts a through d below. a) Find the mean and standard deviation of the number of red lights the commuter should expect to hit in her week. The mean is red light(s) and the standard deviation is red light(s). (Round to two decimal places as needed.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
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!
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