The speed of cars passing through the intersection of Blossom
Hill Road and the Almaden Expressway varies from 10 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.
the number of cars passing through the intersectionthe time, in
seconds, it takes a car to pass through the
intersection the speed, in mph, of an
individual car passing through the intersectionthe number of cars
driving below 35 mph through the intersection
Part (b)
Give the distribution of X.
X ~
,
Part (c)
Graph the probability distribution.
Part (d)
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 30 mph? (Enter your answer as a fraction.)
Part (h)
What is the probability that the speed of a car is
between 17 and 23 mph? (Enter your answer as a
fraction.)
Part (i)
State "P(21 < X < 55) =
___" in a probability question.
What is the probability that the speed of a car is between 21
and 55 mph?What is the probability that the speed of a car is
exactly 21 or 55 mph? What is the
probability that the speed of a car is below 21 given that it is
below 55 mph?What is the probability that the speed of a car is
below 21 or above 55 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 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 25 mph given (or knowing that) it is at
least 13 mph. (Enter your answer as a fraction.)