Example 5.1.7 A car-hire firm has two cars, which are hired out everyday.The number of demands for a car on each day is distributed as a Poissondistribution with mean 1.5. Calculate the proportion of days on whichneither car is used and the proportion of days on which a demand cannotbe met due to lack of cars [e15 = 0.2231].

Answered: Image /qna-images/answer/ef32ab39-c2d6-4b46-99f9-bcb1abdd1011.jpg

Answered: Example 5.1.7 A car-hire firm has two…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. The data are weekly averages of fasting blood glucose levels (m mols) of a diabetic patient treated with different doses of insulin (units) given over a period of 32 weeks. To recognize the trend in blood glucose change, 8 weeks from the treatment duration of first 12 weeks were chosen randomly and the data are as follows: Week 4 12 7 6 9 2 11 8 Blood sugar (m/mol): 8.1 4.0 5.3 6.1 5.7 7.3 4.8 4.6 Dose/day (units): 15 55 45 30 35 25 Lost 50 Evaluate the relationships between blood sugar levels and the dose of insulin/day. Describe and interpret this relationship?
EXAMPLE 6.16 A self-service store employs one cashier at its counter. Nine customers arrive on an average 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, find (i) the average number of customers in the system, (ii) the average number of customers in queue or average queue length, (iii) the average time a customer waits before being served, and (iv) the average time a customer spends in the system.
,./
Vehicles arrive at a car detailing service at a rate of 10 per minute according to a Poissondistribution. For simplicity, assume that there is only one lane and one worker who can serve atan average rate of 12 vehicles per minute. Service times are exponentially distributed. Part A: What is the average length of the queue? Part B: What is the average time a vehicle must spend to get through the system? Part C: What is the utilization rate of the worker? Part D: What is the probability that when you arrive at the shop, there will be three ormore vehicles ahead of you?
Matthew the Barber owns a one-chair shop. At barber college, they told Matthew that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Matthew an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Part (b): The average time a customer waits. Part (c): The average time a customer is in the shop. Part (d): The average utilization of Matthew's time.
Example 9.27 The average daily sales of 500 branch officials was Rs 1,50,000 and the standard devia- tion was Rs 15,000. Assuming the distribution to be normal, indicate how many branches have sales between: (i) Rs 1,20,000 and Rs 1,45,000 (ii) Rs 1,40,000 and Rs 1,65,000 (iii) More than Rs 1,65,000
Only 2.4
4.3
1. The data in Table 7–6 were collected in a clinical trial to evaluate a new compound designed to improve wound healing in trauma patients. The new compound was com- pared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing was measured. Is there a difference in the extent of wound healing between the treatments? (Hint: Are treatment and the percent wound healing independent?) Run the appropriate test at a 5% level of significance. Use the data in Problem 1. Pool the data across the treatments into one sample of size n = 250. Use the pooled data to test whether the distribution of the percent wound healing is approximately normal. Specifically, use the following distribution 30%, 40%, 20%, and 10% and a = 0.05 to run the appropriate test. Percent Wound Healing Treatment 0-25% 26-50% 51-75% 76-100% New compound (n=125) 15 37 32 41 Placebo (n=125) 36 45 34 10
Example57. From the following cumulative distribution of marks obtained by 22 students calculate mode: Marks below 10 20 30 40 50 No. of students 3 8. 17 20 22 Ma No. G
Consider the rate of return of stocks ABC and XYZ. Year 1 2 SAWN T 3 4 5 FABC 24% 10 17 4 1 ABC XYZ a. Calculate the arithmetic average return on these stocks over the sample period. (Round your answers to 2 decimal places.) rxyz 34% 12 18 1 -9 Arithmetic Average ABC XYZ % % b. Which stock has greater dispersion around the mean return?
Question 4 Multi-Server QueueA supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 3 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per hour.a. What is the minimum number of cashers that would be needed to have the utilization less than one?b. If the waiting time is too long, customers might leave the store or even do not enter the store. It is estimated that for every minute of waiting time, the supermarket loses a potential profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD / hour. How many cashers should the supermarket employ to maximize its profit? (Keep four decimal places.

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