suppose that there are two types of busses, red ones arrive at rate λred per minute,...

suppose that there are two types of busses, red ones arrive at rate λ_red per minute, blue ones arrive at rate λ_blue per minute, and all busses arrive independently of each other

Find the probability that:

(a) the first red bus arrives before the first blue bus.

(b) the second red bus arrives before the second blue bus

Expert Solution

milcah answered 1 month ago

Customers arrive at a local grocery store at an average rate of 2 per minute. (a)...

Customers arrive at a local grocery store at an average rate of 2 per minute. (a) What is the chance that no customer will arrive at the store during a given two minute period? (b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons? (c)...

Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that...

Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that the number of customer arrivals X follows a Poisson distribution. A. Find the probability of more than 25 people arriving within the next two hours using the Poisson mass function. B. Find the probability of more than 25 people arriving within the next two hours using the normal approximation to the Poisson. C. Compute the percent relative difference between the exact probability computed in...

Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the...

Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. Part a) What is the probability that exactly two customers arrive in a minute? Part b) Find the probability that more than three customers arrive in a two-minute period. Part c) What is the probability that at least seven customers arrive in three minutes, given...

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the...

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. Part a) What is the probability that exactly two customers arrive in a minute? Part b) Find the probability that more than three customers arrive in a two-minute period. Part c) What is the probability that at least seven customers arrive in three minutes, given...

Airline passengers arrive randomly and independently at the passenger check-in counter. The average arrival rate is 10 passengers per minute.

POISSON PROBABILITY DISTRIBUTION Airline passengers arrive randomly and independently at the passenger check-in counter. The average arrival rate is 10 passengers per minute. to. Calculate the probability that no passenger will arrive within one minute. μ = 10 in 1 minute x = 0 in 1 minute b. Find the probability that three or fewer passengers will arrive within one minute. μ = 10 in 1 minute x ≤ 3 in 1 minute >>> P (x = 0) + P...

Voters arrive at a polling station at an average of 9 per minute (Poisson) where the...

Voters arrive at a polling station at an average of 9 per minute (Poisson) where the service rate is 150 per hour (Poisson). What is the average number of voters in the system with 4 voter booths? (10 pts) What is the minimum number of voting booths needed to keep the average time in the system under 1 minute (must show time)? (10 pts)

Measure heart rate in beats per minute, respiration rate in breaths per minute and blood pressure...

Measure heart rate in beats per minute, respiration rate in breaths per minute and blood pressure as systolic/diastolic (these measurements should look like 120/70). Your pulse rate should be measured for at least 15 seconds and your respiration rate should be measured for at least 30 seconds. Try taking your blood pressure as quickly as you can. Perform the following experiments and enter your data on the Report Page. 1. While you are resting, either or sitting or lying down,...

A bag contains two red marbles, four green ones, one transparent one, two yellow ones, and...

A bag contains two red marbles, four green ones, one transparent one, two yellow ones, and three orange ones. You select three at random. Compute the probability of the given event. (Enter your probability as a fraction.) At least one is not red.

Customers arrive at a two pump system at Poisson rate two per hour. An arrival finding...

Customers arrive at a two pump system at Poisson rate two per hour. An arrival finding the system empty is equally likely to enter service with either pump. An arrival finding one customer in the system will enter service with the idle pump. An arrival finding two others in the system will wait in line for the first free pump. An arrival finding three in the system will not enter. Two service times are exponential with rates one per hour...

Patients are arriving at a clinic at a rate of two per minute. Each patient’s visit...

Patients are arriving at a clinic at a rate of two per minute. Each patient’s visit consists of four steps: check in, record vital signs, receive treatment, and check out. A receptionist takes 1 minute to check a patient in. A nurse takes 2 minutes to record the patient’s vital signs. A doctor spends 10 minutes with a patient. A staff member takes 3 minutes to check a patient out. What is the cycle time of the process in minutes?

Question