Question

The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway varies from 12 to 35 mph and is uniformly distributed. None of the cars travel over 35 mph through the intersection.

a. In words, define the Random Variable X.

b. Give the distribution of X.

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

f(x)= ? where <or equal to X <or equal to

e. Enter an exact number as an integer, fraction, or decimal.
μ =

f. σ =  (rounded to two decimal places)

g. What is the probability that the speed of a car is at most 28 mph? (Enter your answer as a fraction.)

h. What is the probability that the speed of a car is between 18 and 23 mph? (Enter your answer as a fraction.)

i. State "P(19 < X < 52) = ___" in a probability question. and find the probability. (Enter your answer as a fraction.)

j. Find the 90th percentile.

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

k. Find the 75th 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.

l. Find the probability that the speed is more than 29 mph given (or knowing that) it is at least 15 mph. (Enter your answer as a fraction.)

Answer 1

a) X is speed of a randomly chosen car on intersection of Blossom Hill Road and the Almaden Expressway .

b)

X ~U(12,35)

d(

f(x) =1/(35-12)=1/23

e)

mean μ=(a+b)/2 =

23.5

f)

standard deviation σ=(b-a)/√12=

6.64

g)

P(X<28)=(28-12)/(35-12)=16/23

h)

P(18<X<23)=(23-18)/(35-12)=5/23

i)

probability that the speed of a car is between 19 and 52 mph

P(19<X<52) =P(19<X<35)=(35-19)/(35-12)=16/26

j)

90th percentile =12+90*(35-12)/100=32.7

This means that 90% of the time, the speed is less than 32.7 mph while passing through the intersection.

k)

75th percentile =12+75*(35-12)/100=29.25 This means that__24___% of the time, the speed is less than __29.25__ mph while passing through the intersection.

l)

P(X>29|X>15) =(35-29)/(35-15) =6/20 =3/10