Question

For each probability and percentile problem, draw the picture.

The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway varies from 15 to 35 mph and is uniformly distributed. None of the cars travel over 35 mph through the intersection.

Part (i)
State "P(19 < X < 59) = ___" in a probability question.
What is the probability that the speed of a car is exactly 19 or 59 mph?
What is the probability that the speed of a car is below 19 or above 59 mph?
What is the probability that the speed of a car is between 19 and 59 mph?
What is the probability that the speed of a car is below 19 given that it is below 59 mph?

Draw the picture and find the probability. (Enter your answer as a fraction.)

Part (j)
Find the 60th percentile.
This means that 60% of the time, the speed is less than
mph while passing through the intersection.

Part (k)
Find the 65th percentile. In a complete sentence, state what this means.
This means that
% of the time, the speed is less than
mph while passing through the intersection.

Part (l)
Find the probability that the speed is more than 27 mph given (or knowing that) it is at least 20 mph. (Enter your answer as a fraction.)

Answer 1

i)

What is the probability that the speed of a car is between 19 and 59 mph

probability =(35-19)/(35-15)=16/20=0.8

j) 60th percentile =15+0.6*(35-15)=27

This means that 60% of the time, the speed is less than
27 mph while passing through the intersection.

k)

65th percentile =15+0.65*(35-15)=28

This means that
65% of the time, the speed is less than 28
mph while passing through the intersection.

l)

probability that the speed is more than 27 mph given it is at least 20 mph

=P(X>27|X>20)=(35-27)/(35-20)=8/15