The distance it takes Georges car to stop at a certain speed

The distance it takes George\'s car to stop at a certain speed once the brakes are applied varies evenly between 20 and 55 feet. Let 5 be the distance it takes for George\'s car to stop at this speed. Find the distribution, parameter(s), and support of S. What is the probability that it takes between 15 and 28 feet for the car to stop at this speed? Find the expected distance it will take George to stop and the standard deviation of the stopping distance. What is the 45th percentile of George\'s stopping distances at this speed? Suppose a squirrel decides to dart into the road as George is driving this speed, and when George finally sees the squirrel and applies the brakes, the squirrel is 31 feet away. What is the probability that the squirrel survives its encounter with George (i.e. that George stops before he hits the squirrel)? George is out driving at this speed when it begins to rain. George knows that when it rains, it will take a minimum of 27 feet to stop. If there is a stop sign that is 35 feet away, what is the probability that George stops in time?

Solution

X , the distance George car stops after brake is applied is uniform in [20,55] PDF of x 1/35, 20