Service calls arriving at an electric company follow a Poisson distribution with an average arrival rate...

Service calls arriving at an electric company follow a Poisson distribution with an average arrival rate of 70 per hour. Using the normal approximation to the Poisson, find the probability that the electric company receives at most 58 service calls per hour. Round your answer to four decimal places, if necessary.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose that telephone calls arriving at a particular switchboard follow a Poisson process with an average...

Suppose that telephone calls arriving at a particular switchboard follow a Poisson process with an average of 6 calls coming per minute. What is the probability that up to 2 minutes will elapse by the time 2 calls have come into the switchboard?

telephone calls arrive at an exchange have a poisson distribution at an average rate of one...

telephone calls arrive at an exchange have a poisson distribution at an average rate of one every second. Find the probabilities of the following; a. no calls arriving in a given five-second period b. between four and six calls arriving in the five-second period c. there is atleast one call d. there is at most one call

The number of emails arriving at a server per minute is claimed to follow a Poisson distribution.

The number of emails arriving at a server per minute is claimed to follow a Poisson distribution. To test this claim, the number of emails arriving in 70 randomly chosen 1-minute intervals is recorded. The table below summarizes the result. Number of emails 0 1 2 ≥ 3 Observed Frequency 13 22 23 12 Test the hypothesis that the number of emails per minute follows a Poisson distribution? Use a significance level of α...

Suppose the number of customers arriving at a store obeys a Poisson distribution with an average...

Suppose the number of customers arriving at a store obeys a Poisson distribution with an average of λ customers per unit time. That is, if Y is the number of customers arriving in an interval of length t, then Y∼Poisson(λt). Suppose that the store opens at time t=0. Let X be the arrival time of the first customer. Show that X∼Exponential(λ).

The number of people arriving at an emergency room follows a Poisson distribution with a rate...

The number of people arriving at an emergency room follows a Poisson distribution with a rate of 9 people per hour. a) What is the probability that exactly 7 patients will arrive during the next hour? b. What is the probability that at least 7 patients will arrive during the next hour? c. How many people do you expect to arrive in the next two hours? d. One in four patients who come to the emergency room in hospital. Calculate...

The number of people arriving at an emergency room follows a Poisson distribution with a rate...

The number of people arriving at an emergency room follows a Poisson distribution with a rate of 7 people per hour. a. What is the probability that exactly 5 patients will arrive during the next hour? (3pts) b. What is the probability that at least 5 patients will arrive during the next hour? (5pts) c. How many people do you expect to arrive in the next two hours? (4pts) d. One in four patients who come to the emergency room...

Suppose that telephone calls arriving at a particular switchboard follow a Poisson process with an average of 5 calls coming per minute. What is the probability that up to a minute will elapse by the time 2 calls have come in to the switchboard?

Suppose that telephone calls arriving at a particular switchboard follow a Poisson process with an average of 5 calls coming per minute. What is the probability that up to a minute will elapse by the time 2 calls have come in to the switchboard?

A queuing system with a Poisson arrival rate and exponential service time has a single queue,...

A queuing system with a Poisson arrival rate and exponential service time has a single queue, two servers, an average arrival rate of 60 customers per hour, and an average service time of 1.5 minutes per customer. Answer the following questions. Show ALL formulas and calculations used in your response. The manager is thinking of implementing additional queues to avoid an overloaded system. What is the minimum number of additional queues required? Explain. How many additional servers are required to...

A queuing system with a Poisson arrival rate and exponential service time has a single queue,...

A queuing system with a Poisson arrival rate and exponential service time has a single queue, two servers, an average arrival rate of 60 customers per hour, and an average service time of 1.5 minutes per customer. The manager is thinking of implementing additional queues to avoid an overloaded system. What is the minimum number of additional queues required? Explain. How many additional servers are required to ensure the utilization is less than or equal to 50%? Explain. If the...

The number of arriving customers to a big supermarket is following a Poisson distribution with a...

The number of arriving customers to a big supermarket is following a Poisson distribution with a rate of 4 customers per a minute. What is the probability that no customer will arrive in a given minute? What is the probability that exactly 3 customers will arrive in a given minute? What is the probability that at least seven customer will arrive in a given minute? What is the probability that at most one customer will arrive in 40 seconds? What...

Subjects