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12 June, 13:49

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.

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  1. 12 June, 17:26
    0
    The probability is 82.64, Given this probability, lights should be installed because they exceed the 80% limit.

    Step-by-step 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.
  2. 12 June, 17:32
    0
    Step-by-step 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.
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