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14 March, 13:35

Imagine that a traffic intersection has a stop light that repeatedly cycles through the normal sequence of traffic signals (green light, yellow light, and red light). In each cycle the stop light is green for 30 s, yellow for 3 s, and red for 50 s. Assume that cars arrive at the intersection uniformly, which means that in any one interval of time, approximately the same number of cars arrive at the intersection at any other time interval of equal length. Determine the probability that a car arrives at the intersection while the stop light is yellow. Give your answer as a percentage precise to two decimal places.

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  1. 14 March, 15:48
    0
    3.61%

    Step-by-step explanation:

    To know the statistics we have to realize that there are 3 options.

    green 30s

    yellow 3s

    red 50s

    As each color does not have the same time, we will take the seconds to solve it

    first we calculate all the seconds of a cycle

    30s + 3s + 50s = 83s

    the car that arrives will always arrive in some second of those 83 seconds

    now of those 83 seconds only 3 seconds the traffic light will be yellow

    we make the events that meet the condition on the possible

    3s/83s = 3/83

    to express it as a percentage, we divide it by 83 and multiply it by 100

    100 * (3/83) / 83 = 3.614457831%

    we have to round with two decimal

    3.61%
  2. 14 March, 16:35
    0
    Your answer is 3.61%.
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