Q1- Customers are used to evaluate preliminary product design. In the past, 95% of highlysuccessful products received good reviews, 60% of moderately successful products receivedgood reviews, and 10% of poor products received good reviews. In addition, 45% of productshave been highly successful, 30% have been moderately successful, and 25% have been poorproducts.a- What is the probability that a product attains a good review?b-If a new design attains good review, what is the probability that it will be a highlysuccessful product?c-If a product does not attain a good review, what is the probability that it will be a highlysuccessful product?Q2- Messages arrive to a computer server according to a Poisson distribution with a mean rateof 5per hour.a- Determine the probability that at least three messages arrive during 2 hours.b- Determine the probability that exactly two messages arrive in one hour.c-Determine the length of an interval of time such that the probability that no messagearrive during this interval is 0.9.Q3- The dimeter of the dot produced by a printer is normally distributed with a mean dimeter of0.004 cm and standard deviation of 0.001 cm.a- What is the probability that the diameter of a dot exceeds 0.0062 cm?b- What is the probability that the diameter is between 0.0031 and 0.0064?What standard dev tion of dimeters is needed soC-the probability in part(a) is 0.95?

Let us define some events A : a product is highly successful. B : a product is moderately…

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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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- What is the probability that a product attains a good review? - If a new design attains good review, what is the probability that it will be a highly successful product? - If a product does not attain a good review, what is the probability that it will be a highly successful product?