2. The number of cars passing through a road in 1 minute follows a Poisson Distribution...
The number of cars passing through the M50 toll follows a Poisson distribution with a rate of lambda = 90000 cars per day. What is the probability that more than 187950 euro is collected in tolls on a given day? (correct to 4 decimal places)
2. The number of cars passing through each lane of a toll booth per minute is represented by a random variable, C, and the number of trucks passing through it is represented by another random variable, T. During the morning peak hour, the joint probability mass function of C and T is given by the following table 0 0.05 0.08 0.08 1 0.05 0.09 0.11 0.08 0.22 0.11 0.06 0.05 0.02 Find the marginal probability mass function of T, pr(t)...
Suppose the number of phone calls passing through a particular cellular relay system, follows a Poisson distribution with an average of 3 calls during a 1-min period. (A) Find the probability, p, that no call will pass through the relay system during a given 2-min period. (B) Find the probability that at least four minutes will pass before a call is passed through the relay system.
Poisson The number of cars arriving at a given intersection follows a distribution with a mean rate of 1 per second. What is the probability that no cars arrive within a 3-second interval? (A) 1/e3 (B) 2/e3 (C)3/e3 (D) 4/e3 (E) None of these
The number of automobiles entering a tunnel per 2-minute period follows a Poisson distribution. The mean number of automobiles entering a tunnel per 2-minute period is four. (A) Find the probability that the number of automobiles entering the tunnel during a 2minute period exceeds one. (B) Assume that the tunnel is observed during four 2-minute intervals, thus giving 4 independent observations, X1, X2, X3, X4, on a Poisson random variable. Find the probability that the number of automobiles entering the...
1. The random variable X follows a normal distribution N(10,1). Using the provided table to find prob( (X-10)2 4) Patients arrive at a clinic at an average rate of 300 per hour. Assume the arrival at each minute follows a Poisson distribution 2. a. b. c. Find the probability that none passes in a given minute. What is the expected number passing in two minutes? Find the probability that this expected number actually pass through in a given two-minute period.
Assume the number of cars that drive through the Mooncents Coffee Shop drive-through window follows a Poisson probability process with a known average of 6 cars per hour (per 60 minutes). a. Find the expected number of cars driving though in a 23 minutes period. (Round your final answer to 1 decimal place.) Expected number of cars b. Find the probability of at least 2 cars driving through in a given 23 minutes period. (Round your answer to 4...
The number of visitors to a webserver per minute follows a Poisson distribution. If the average number of visitors per minute is 4, what is the probability that: (i) There are two or fewer visitors in one minute? (2 points) (ii) There are exactly two visitors in 30 seconds? (2 points)
Question 3 The number of messages in certain corporate mailbox follows a Poisson distribution with a mean rate of 4 per minute. What is the probability that more than 9 messages are received in that mailbox in 2 minutes? Round your answers to at least two decimals.
Question 3: The number of cars arrive at a gas station follows a Poisson distribution with a rate of 10 cars per hour. Calculate the probability that 2 to 4 (inclusive) cars will arrive at this gas station between 10:00 am and 10:30 am. What are the mean and standard deviation of the distribution you have used to answer part a?