Question

In: Operations Management

Roberta’s Auto Repairs averages 2.5 hours per repair, exponentially distributed. On average 2.1 customers arrive per...

Roberta’s Auto Repairs averages 2.5 hours per repair, exponentially distributed. On average 2.1 customers arrive per eight-hour day. HINT: To calculate the measures per day, convert the service time (number of hours) to service rate per day.

a.	Calculate the average number of automobiles that are waiting to be fixed. (Round your answer to 2 decimal places.)

Number of automobiles

b.	Calculate system utilization. (Round your answer to the nearest whole percent, but do not type the percent sign.)

System utilization

%

c.	Calculate the amount of time during a day that Roberta is not working on a repair. (Round your answer to 2 decimal places.)

Amount of time

hours

d.	Calculate the probability of two or more repairs in the system. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Probability

Expert Solution

(a) The average number of automobiles that are waiting to be fixed is 1.26 automobiles.

(b) System Utilization - 0.66

(c) The amount of time during a day that Roberta is not working on a repair is 2.72 hours.

(d) The probability of two or more repairs in the system is 0.4306.

keosha answered 7 months ago

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...

At Baywatch City Airport 3 passengers per minute arrive on average. Inter-arrival times are exponentially distributed....

At Baywatch City Airport 3 passengers per minute arrive on average. Inter-arrival times are exponentially distributed. Arriving (actually departing) passengers go through a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of 3 passengers per minute, where the time to check a passenger is also exponentially distributed. Why is this an M/M/1,...

Customers arrive at the rate of 100 per hour. The ticket seller averages 30 seconds per...

Customers arrive at the rate of 100 per hour. The ticket seller averages 30 seconds per customer. What is the average customer time in the system?

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...

During the early morning hours, customers arrive at a branch post office at an average rate...

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Fill in the following information: Lq = Avg Number in Line Wq = Avg Time in Line Ws = Avg Time in System For M = 7: Lq = 0.028 Wq = 0.0006 Hours Wq = 0.0373 Minutes Ws = 4.0373 Minutes For M =...

Cars arrive at Carla’s Muffler Shop for repair work at an average of 3 per hour,...

Cars arrive at Carla’s Muffler Shop for repair work at an average of 3 per hour, following an exponential distribution. (a) What is the expected time between arrivals? (b) What is the variance of the time between arrivals? Use Appendix C

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)...

Customers arrive at a local ATM at an average rate of 14 per hour. Assume the...

Customers arrive at a local ATM at an average rate of 14 per hour. Assume the time between arrivals follows the exponential probability distribution. Determine the probability that the next customer will arrive in the following time frames. a) What is the probability that the next customer will arrive within the next 2 minutes? b) What is the probability that the next customer will arrive in more than 15 minutes? c) What is the probability that the next customer will...

The lifetime of a certain kind of battery is exponentially distributed, with an average lifetime of...

The lifetime of a certain kind of battery is exponentially distributed, with an average lifetime of 25 hours 4. Find the value of the 60th percentile for the lifetime of one battery. Remember units! 5. Write an interpretation (a sentence) of the 60th percentile for the lifetime of one battery. Your interpretation should include the value of the 60th percentile with correct units. 6. We are interested in the average lifetime of 16 of these batteries. Call this random variable....

Clients arrive at a law office with a single lawyer at a rate of 2.5 per...

Clients arrive at a law office with a single lawyer at a rate of 2.5 per hour. The lawyer takes an average of 10 minutes with each client. Assuming that arrivals are Poisson distributed and the legal service time is exponentially distributed, answer the following questions: a.) Compute that answers for this problem using the first six queuing equations. b.) Service goals for this law office dictate that an arriving client should not have to wait more than an average...