In a certain factory, machines I, II, and III are all producing springs of the sameQ.2.length. Machines I, II, and III produce 3%, 2%, and 5% defective springs, respectively. Of thetotal production of springs in the factory, Machine I produces 30%, Machine II produces 25%, andMachine III produces 45%. If one spring is selected at random from the total springs produced ina given day, determine the probability that it is defective.

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Answered: In a certain factory, machines I, II,…

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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2. All of Dave's customers are neighbors that have yards of about the same size. Dave charges a flat rate of $32 for mowing and trimming and $20 for just mowing. Based on experience, he determines that the probability that a randomly selected customer wants him to mow and trim the lawn is 0.85; the rest of his customers just want him to mow. Let C= the amount Jacob charges a randomly selected customer. (a) Make a table that shows the probability distribution of C. (b) Calculate and interpret the mean of C. (c) Calculate and interpret the standard deviation of C. opp
PART C. 1. James is an operator of a machine that uses 16 batteries. Because it has so many, it does not shut off until half of the batteries are dead. a. All batteries are independent and have uniformly distributed lifetimes on the interval [ 0, 1 2] years. Find the probability that the machine shuts before 1 years of work? b. What is the expected time when the 5th and the 8th battery die?
Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light. Traffic light A Traffic light B Traffic light C ?(?)P⁡(A) ?(?)P⁡(B) ?(?)P⁡(C) 0.6 0.4 0.9 What is the probability that the employee is not late for work? (Round to 3 decimal places)
A study of the incoming freshman class at a university found that 60% of the students had taken AP Calculus in high school, 55% had taken AP English in high school, and 20% had taken both AP Calculus and AP English. One incoming freshman is randomly selected from the population of incoming freshman. Let: C = the selected student took AP Calculus E = the selected student took AP English What is the probability that the selected incoming freshman took AP English or AP Calculus, i.e. P( C or E)? 0.15 O 0.75 0.80 0.05 0.95
A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (20+I)%, and (10+H)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2? H is 3 and I is 2
This circuit operates only if there is a path of functional devices from left to right (a to b). If the probability that each device functions is 0.95, what is the probability that the circuit operates? Each device fails independently. 1 4 a 7 2
Consider an M/M/1 queuing system with mean inter arrival time of 4 minutes. The average service time for each customer is 3 minutes. The probability that there are 3 arrivals in the system is closest to O a. None of these O b. 0.105 Oc. 0.895 O d. 0.422
Consider three classes (I, II and III) consisting of 30, 25, and 45 students. Suppose a student is selected from class I, then he has 10% chance to make an A. Assume that these probabilities for the class II and III are 15% and 20% respectively. If a student is selected randomly and has an A, what is the probability that he is from class III. Enter your answer to the nearest FOUR decimal places. 0.5715
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 7 customers per hour and an average service rate of 12 customers per hour. The probability of 2 customers in the system is : a. 0.1418 b. 0.6597 C. 0.4167 d. 0.8582
A system consists of four components connected as shown below in the following diagram.Assume ?, ?, ?, and ? function independently. If the probability that ?,?, ?, and ? fail are 0.10, 0.05, 0.10, and 0.20 respectively. What is the probability that the system functions?b) A process manufactures ball bearing whose diameters are normally distributed with mean 2.505?? and standard deviation 0.008??. Specifications call for the diameter to be in the interval 2.5 ± 0.01 cm. what proportion of the ball bearings will meet the specification

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