Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ = 20 (suggested in the article "Dynamic RideSharing: Theory and Practice"+). (Round your answer to three decimal places.)(a) What is the probability that the number of drivers will be at most 15?0.1572(b) What is the probability that the number of drivers will exceed 27?0.8168X(c) What is the probability that the number of drivers will be between 15 and 27, inclusive?0.7698XWhat is the probability that the number of drivers will be strictly between 15 and 27?0.8439X(d) What is the probability that the number of drivers will be within 2 standard deviations of the mean value?You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answered: Suppose that the number of drivers who…

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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The number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55. Suppose that the random variable X is the number of earthquakes occurring in one day in the world. Let the random variable Y be the total number earthquakes occurring in the world in 3 days. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.a. For our model, what is expected value of X? b. What is the probability that X = 55? c. What is the probability that X > 55? d. What is the probability that X >60? e. What is the smallest value C so that there is at least a 0.9 probability of no more than C earthquakes in a day? f. Y also has a Poisson distribution. What is the parameter ?y for Y? g. What is the standard deviation of X? h. What is the probability Y =164? i. What is the probability that Y < 164? j. What is the probability that X>60 given that X>55?
Q1. Please answer the question with details.
The mean number of customers arriving at a service station during the 25-minute period is 5. Find the probability that 3 or more customers will arrive at the service station during a 25-minute period. Assume that the service system can be modeled as a Poisson distribution
E The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is
8. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson distribution is a suitable model, find the probability that less than 3 hurricanes in a randomly selected year. O a. .1901 O b. None of the above O C. .2075 O d. .3701 O e..1016 日田

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.
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
4. Suppose that 60% of college students own a smart phone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here?
An online advertisement is viewed 1.1 times per hour an average. The number of views per hour follows a Poisson distribution. Find the probability that the advertisement will be viewed more than 2 times in a randomly selected hour. (Provide your answer as a number between 0 and 1 rounded to 3 decimal places.)
Question 15
What do i specifically put in the box as p(x)=
(c) Does this Poisson distribution provide a good model for the number of accidents in this example (as per Table 1)? Explain why or why not. Use R to produce a graph to help support your answer (produce the R as part of your answer). (d) Use the model in (b) to estimate the probability that less than 2 accidents were recorded in any randomly chosen week. How does this compare to the actual data?

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