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 ft. a. What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement

6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

Poisson distribution with a mean of 1 crack per 100 ft.

So , in which ft is the length of the pavement.

What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement

500ft, so

This is P(X = 8).

6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement

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