Question

The New York Transportation Department issued a report indicating that over the past year 234 accidents occurred at the intersection of Broad Street and Pine Street. The Transportation Department has indicated that a traffic light will be installed if there is at least an 80% probability of more than two accidents at this intersection in any given week. You are asked to statistically determine if a light will be installed.

Answer 1

Explanation:

The New York Transportation Department issued a report indicating that over the past year 234 accidents occurred at the intersection of Broad Street and Pine Street.

There was a total of 234 accidents in the past year. For a traffic light to be installed, there is at least an 80% probability of more than two accidents at this intersection in any given week.

In a year, there are 56 weeks, thus 234 accidents / 56 = 4.5

p (x> 2) = (1-p) (x <= 2)- the probability of having more than 2 accidents per week

An average of four is more than the 80% probability of more than two accidents, thus a traffic light should be installed.

Answer 2

The probability is 82.64, Given this probability, lights should be installed because they exceed the 80% limit.

Explanation:

according to the exercise we can have the data that

the number of accidents per year = 234

then we will look for the number of accidents per week obtaining:

234/52 = 4.5

the probability that more than 2 accidents will occur at most would be

p (x> 2) = 1-p (x <= 2)

replacing the data we get that

1- (p (x = 0) + p (x = 1) + p (n = 2))

= 1-0.1736 = 0.8264

we convert to a percentage and the answer is 82.64%

Given this probability, lights should be installed because they exceed the 80% limit.