Use the following data to construct a headway distribution curve. If the minimum gap accepted is 3.0 seconds, determine the probability that a vehicle approaching on a side street will have to wait more than 3 gaps before merging into traffic

Vehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than 8 seconds is

4. The statistical data of an urban spot speed study is given below. A set of 130 observations of spot speeds made by timing vehicles through a "Trap" of 88ft. The stopwatch was used to obtain data. The stopwatch data are grouped into 0.2 sec. Classes. The first column of the table shows the midpoint of each group. The second column of the table shows the frequency of the observations. Compute the following statistical values. a) The speed of each time class in mph (show it in the third column) b) The cumulative percent of vehicles traveling at or below indicated speed shown in the third column in mph (show it in the forth column) c) Mean or average speed (time-mean speed), median, mode, standard deviation, standard error of the mean, average time, space-mean speed, variance, 15%, and 85% speed. d) Plot the cumulative percentage, and show the statistical values of item (c) on the graph. e) Plot the frequency distribution curve and show the statistical values on the graph.