1. The distance it takes George’s car to stop at a certain speed once the brakes

Question

1. The distance it takes George’s car to stop at a certain speed once the brakes are applied varies evenly between 20 and 75 feet. a) Let S be the distance it takes for George’s car to stop at this speed. Find the distribution, parameter(s), and support of S. b) What is the probability that it takes between 32 and 58 feet for the car to stop at this speed? c) Find the expected distance it will take George to stop and the standard deviation of the stopping distance. d) What is the 45th percentile of George’s stopping distances at this speed? e) Suppose a squirrel darts into the road as George is driving this speed, and when George finally sees the squirrel and applies the brakes, the squirrel is 42 feet away. What is the probability that the squirrel survives its encounter with George (i.e. that George stops before he hits the squirrel)?

Explanation / Answer

a) here it is uniform distribution with parameter a=20 and b=75, with support of S=U[a,b] =[20.75]

b) probability that it takes between 32 and 58 feet =P(32<X<58)=(58-32)/(75-20)=0.4727

c) expected distance =(a+b)/2 =(20+75)/2=47.5

std deviation =(b-a)/(12)1/2 =(75-20)/(12)1/2 =15.877

d) 45th percentile =20+0.45*(75-20)=44.75

e)probability that the squirrel survives its encounter with George=P(X<42)=(42-20)/(75-20)=0.4

please revert for any clarificaiton required.

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