Question

The number of accidents per week at a hazardous intersection varies with mean of 2.2 accidents and a standard deviation 1.4. This distribution takes on only whole number values, so it is certainly not normal. a) Let x be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of x (consider the year to be a random sample of size 52)?

Answer 1

X follows Poisson with mean= 2.2 accidents per week

Parameter of the distribution = 2.2

Explanation:

Given that the number of accidents per week at a hazardous intersection varies with mean of 2.2 accidents and a standard deviation 1.4.

Since number of accidents is discrete, this is a discrete distribution.

X is the mean number of accidents per week at the intersection during a year (52 weeks).

We have to find the approximate distribution of X

Since accidents are less compared to the total vehicles here no of vehicles passing through would be large with probability for accident very small such that the product is finite.

Hence this is a case of Poisson distribution

X follows Poisson with mean= 2.2 accidents per week

Parameter of the distribution = 2.2