8. An automobile manufacturer is concerned about a fault in the braking mechanism ofa particular model. The fault can, on rare occasions, cause a catastrophe at highspeed. The distribution of the number of cars per year that will experience the faultis a Poisson random variable withA- 5.a) What is the probability that at most 3 cars per year will experience acatastrophe?b) What is the probability that more than 1 car per year will experience acatastrophe?

X:number of cars per year that will experience the fault. X~poission(λ) where λ=5 probability mass…

Answered: 8. An automobile manufacturer is…

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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10. The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 6 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period.e. Calculate the probability that there will be a failing student within the first semester.f. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?
Power failures occur at an electric plant on average 3 times per year. If we can assume this follows a Poisson distribution, answer the following questions. a. What is the probability that there are 4 power failures in 2021? b. What is the probability that there are no more than 2 power failures in a given year? c. How likely is it that there are at least 3 power failures next year?
13. In a certain population, heights (in inches) are normally distributed with a = 67 and a = 3. Find the probability that a person selected at random has a height between 63 and 71 inches. Refer to Appendix A of the textboun. -
5. Suppose that the number of insects caught in a spider's web in one day follows a Poisson distribution with rate = 2.6. For the questions that follow, make sure to define a random variable, state its distribution (including parameters), and translate the question into a probability statement. %3D wg probal b What is the probability that the spider catches at least one insect in 12 hours? PUS 18)
23.
6. The life expectancy of a brand of car motors has a normal distribution with "- 75,000 and o - 5,500. a. Find the probability that 1 motor is chosen at random will have a life expectancy of more than 90,000 miles.
3
Part 1 of 6 Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The number of light bulbs that burn out in the next year in a room with 13 bulbs b. The hair color of adults in the United States c. The number of pigeons in a country d. The time it takes for a light bulb to burn out e. The number of free-throw attempts before the first shot is missed f. The number of people in a restaurant that has a capacity of 150 ..... a. Is the number of light bulbs that burn out in the next year in a room with 13 bulbs a discrete random variable, continuous random variable, or not a O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable.
5. A new type of car tires is released on the market with rate of tire cracking: on average one crack every 2000km. (a) What is the probability that a randomly chosen tire will cover a distance of 500km without a single crack? (b) How many tires are expected to have two ore more cracks within a distance of 500km?
2.6
7. If three coins are tossed find the expectation of the variance of the number of heads.
A certain model of an automobile is having a fault in the braking mechanism after sale. This is a very serious failure with catastrophic results at high speed. The distribution of the number of cars per year that will experience the fault is found to be a random variable with x=5. a) What is the probability that at most 3 cars per year will experience a catastrophe ? b) What is the probability that more than 1 car per year will experience a catastrophe ?

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