please answer this question: (a) In a manufacturing process, the diameter of steel rods is distributed normally with a mean value of 5 mm and standard deviation of 0.1 mm. If a rod is selected at random, what is the probability that its diameter will be: (i) less than 4.85 mm; (ii) between 4.9 mm and 5.1 mm?

please answer this question: (a) In a manufacturing process, the diameter of steel rods is distributed normally with a mean value of 5 mm and standard deviation of 0.1 mm. If a rod is selected at random, what is the probability that its diameter will be: (i) less than 4.85 mm; (ii) between 4.9 mm and 5.1 mm?

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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Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 90 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 90 tons and standard deviation ? = 1.1 ton. (a) What is the probability that one car chosen at random will have less than 89.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 39 cars chosen at random will have a mean load weight x of less than 89.5 tons of coal? (Round your answer to four decimal places.)
(a) In a manufacturing process, the diameter of steel rods is distributed normally with a mean value of 5 mm and standard deviation of 0.1 mm. If a rod is selected at random, what is the probability that its diameter will be: (i) less than 4.85 mm; (ii) between 4.9 mm and 5.1 mm? (b) A telephone exchange receives an average of 5 calls per minute. Calculate the probability that, in a given minute, the exchange receives: (i) exactly 5 calls; (ii) 2 calls or fewer.
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(A), (B) and (C). Please!
A plant manufactures part whose lengths are normally distributed with a mean of 16.3 centimeters and a standard deviation of 2.5 centimeteres. Question: If one part is randomy selected, find the probability that the part is less than 19.3 centimeters.
Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this information, answer the following questions. (a) What proportion of light bulbs will last more than 60 hours? (b) What proportion of light bulbs will last 50 hours or less? (c) What proportion of light bulbs will last between 58 and 61 hours? (d) What is the probability that a randomly selected light bulb lasts less than 46 hours? (a) The proportion of light bulbs that last more than 60 hours is (Round to four decimal places as needed.) (b) The proportion of light bulbs that last 50 hours or less is (Round to four decimal places as needed.) (c) The proportion of light bulbs that lasts between 58 and 61 hours is (Round to four decimal places as needed.)
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