How many in a car? A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that the number of people per car in the population of all cars that enter at this interchange during rush hours has a mean of u 1.5 and a standard deviation of a 0.75. Could the distribution of the number of people per car be normal for the population of all cars entering the interchange during rush hours? Explain. Describe the shape of the sampling distribution of * for SRSS of size n 100 from the population of all cars that enter this interchange during rush nours. Justify your answer.
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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