13. Suppose that a local appliances shop has found from experience thatthe demand for tubelights is roughly distributed as Poisson with amean of 4 tubelights per week. If the shop keeps 6 tubelights during aparticular week, what is the probability that the demand will exceedthe supply during that week?[Aps:0 1106]

Poisson Distribution : If random variable X follows Poisson distribution with mean λ then…

Answered: 13. Suppose that a local appliances…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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4.4 give the probability data analysis, show solution.
6. Consider a coffee shop that uses a single-server queue. The inter-arrival time is exponentially distributed with a mean of 10 minutes and the service time is also exponentially distributed with a mean of 8 minutes. Calculate the: (i) mean wait in the queue (2) (ii) mean number in the queue (2) (iii) the mean wait in the system (2) (iv) mean number in the system (2) (v) proportion of time the server is idle. (2) [10] 7. The arrival of customers at a bank follows a Poisson distribution with a mean arrival rate of 10 customers per hour. The service time at the bank follows an exponential distribution with a mean service rate of 6 minutes per customer. Calculate the average number of customers in the system (including those being served and waiting) and the average time a customer spends in the system. How is the system performing? [8]
2. An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lives of this particular brand is approximately normal. On the assumption that the claims are true, find the probability that a randomly selected battery of this type will last less than 48 months. (Use the software link for every question) (a) Let X = number of months a battery will last. Write the question above in terms of this variable X (b) Find the probability that a single battery of this type will last less than 48 months. (c) Find the probability that the mean of a random sample of 36 batteries will be less than 48 months. (d) Why do you think the values from part (b) and part (c) are different? Explain.
If you know that every 30 minutes, a plane takes off from Jeddah Airport to Riyadh Airport, starting at 10 am. If a group of passengers arrives at Jeddah airport at a time that follows the regular continuous distribution between 6:00 a.m. and 7:30 a.m., then what is the likelihood that passengers wait for the plane less than 15 minutes
2. Doctors volunteer their time on a daily basis in a clinic. The total number of patients served in a day at the clinic has mean 90 and variance 1890. Determine the probability that 120 or more patients can be served in a day at the clinic. Use the Central Limit Theorem with continuity correction. Use linear interpolation with the normal distribution to find the probability.
For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 515 and a standard deviation of 175. The grading process of this year's exam has just begun. The average score of the 40 exams graded so far is 518. What is the probability that a sample of 40 exams will have a mean score of 518 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. Sub Continue
5. A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average. a. What is the cumulative distribution function of the time until failure? b. What is the probability that a transducer chosen at random functions for eight years without failure? irteen Reliability and Maintainability c. What is the probability that a transducer that has functioned for eight years con- tinues to function for another eight years?
Chains "A" and "B" are made of the same steel. "A" consists of three links and "B" consists of six links, each link having a normal distribution function of the resisting strength with a mean of 60,000 psi and standard deviation of 5,000 psi. Determine which chain is generally weaker (from a probabilistic point of view) by plotting the probability distribution functions of their resisting strengths on the same diagram.
Suppose the demand for a company’s product in week 1,2, & 3 are each normally distributed. The means are 50, 45, and 65. The standard deviations are 10,5, and 15. Assume these 3 demands are probabilistically independent. Suppose the company has 180 units in stock, and it will not be receiving any more shipments from its supplier for at least 3 weeks. What is the probability that stock will run out during the 3 week period? How many units should the company have in stock, so that it can be 98% certain of not running out during the 3 week period , assuming it will not receive any more shipments during this period?
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