Please help thank you.
1 answer:
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Answer:
There is a 6.07% probability that during next 2 min exactly 5 cars passing an intersection are from state.
Step-by-step explanation:
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
is the Euler number
is the mean in the given time interval.
In this problem, we have that:
A traffic engineer monitors the traffic flowing through an intersection with an average of 6 cars per minute. So in 2 minutes, 12 cars are expected to flow through the intersection.
If 75% of vehiclesare from state, what is the probability that during next 2 min exactly 5 cars passing an intersection are from state?
We want to know how many of these cars are from state. In 2 minutes, 0.75*12 = 9 cars from the state are expected to pass the intersection, so .
We want to find P(X = 2).
There is a 6.07% probability that during next 2 min exactly 5 cars passing an intersection are from state.
Let s = the speed of the slower train in km/hrs+10 = the speed of the faster train in km/hrLet t = time in hrs for the slower train to go 160 kmt-5 = time in hrs for faster train to go 160 km---------------Slower train:(1)
160=s.t
Faster train:(2) 160=(s+10) .(t-.5)From (1)(1) t=160/s
use the relations given in following screenshot and then use quadratic equation.
160=s.t
Faster train:(2) 160=(s+10) .(t-.5)From (1)(1) t=160/s
use the relations given in following screenshot and then use quadratic equation.