a driver passes 4 sets of traffic lights. the random varaible X is the number of traffic lights he has to stop at. the probabilty distribution for x is given:
x 0 1 2 3 4
prob 0.1 0.2 0.3 0.2 0.2
a) find the upper quartile of the number of traffic lights at which the driver has to stop for on a single trip ?
b) The total travel time (T) is the driving time plus the waiting time at traffic lights. The driving time for the trip is 13 minutes and the waiting time at each set of lights the driver has to stop at is 2 minutes. Give an equation relating the total travel time to the
driving time and the number of traffic lights stopped at ?
c) What is the probability that the total trip time is less than 18 minutes?
d) What is the probability that the total trip time is less than 18 minutes?
take a shot. what do you think are the answers?
a) To find the upper quartile of the number of traffic lights the driver has to stop at, we need to calculate the cumulative probability distribution.
First, we need to calculate the cumulative probabilities for each value of x:
Cumulative Probability (P(X<=x)):
0 -> 0.1
1 -> 0.1 + 0.2 = 0.3
2 -> 0.3 + 0.3 = 0.6
3 -> 0.6 + 0.2 = 0.8
4 -> 0.8 + 0.2 = 1.0
The upper quartile is the value that falls at or above the 75th percentile. Since 75% falls between the cumulative probabilities of 0.6 and 0.8, the upper quartile falls between the values of 2 and 3.
b) The total travel time (T) is the driving time plus the waiting time at traffic lights. The equation relating the total travel time to the driving time (13 minutes) and the number of traffic lights stopped at (X) is:
T = 13 + (2 * X)
c) To find the probability that the total trip time is less than 18 minutes, we need to sum the probabilities of each possible value of X multiplied by the respective probabilities.
P(T<18) = P(X=0) * P(T<18|X=0) + P(X=1) * P(T<18|X=1) + P(X=2) * P(T<18|X=2) + P(X=3) * P(T<18|X=3) + P(X=4) * P(T<18|X=4)
d) It seems that you have mentioned question c again. Could you please provide the correct statement for question d?