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 A

In words, define the Random Variable X.

a the number of cars passing through the intersection

b the speed, in mph, of an individual car passing through the intersection  

c the number of cars driving below 35 mph through the intersection

d the time, in seconds, it takes a car to pass through the intersection

Part (b)

Give the distribution of X.

X ~ _________, __________

Enter an exact number as an integer, fraction, or decimal.

f(X) = ______, where______  ≤ X ≤ ________

Part (e)

Enter an exact number as an integer, fraction, or decimal.

μ = ______

Part (f)

σ =_________  (rounded to two decimal places)

Part (g)

What is the probability that the speed of a car is at most 26 mph? (Enter your answer as a fraction.)

Part (h)

What is the probability that the speed of a car is between 16 and 22 mph? (Enter your answer as a fraction.)

Part (i)

State "P(20 < X < 52) = ___" in a probability question.

a What is the probability that the speed of a car is between 20 and 52 mph?

b What is the probability that the speed of a car is exactly 20 or 52 mph?  

c What is the probability that the speed of a car is below 20 or above 52 mph?

d What is the probability that the speed of a car is below 20 given that it is below 52 mph?

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

Part (j)

Find the 90th percentile.

This means that 90% of the time, the speed is less than __________mph while passing through the intersection.

Part (k)

Find the 85th 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.)