The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 m. a. What is the probability that there will be exactly 8 cracks in a 500 m length of pavement b. What is the probability that there will be no cracks in a 100 m length pavement c. Let ? be the distance in meters between two successive cracks. What is the probability density function of ? d. What is the probability that the distance between two successive cracks will be more than 50 m

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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!