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ME3023_Hw1 - ME 3023 Measurements in Mechanical Systems...

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ME 3023 Measurements in Mechanical Systems Homework # 1 Fall 2010 Important Note: Solve the following problems on one side of the Engineering graph paper . Please write all the intermediate steps for partial credit. Start each problem on the separate paper. Due Date: In class on October 13, 2010 (Wednesday) 1. (20 points) Consider the diameters of ball bearings that have a mean value of 4.0 in and a standard deviation of 0.1 in . Assuming that the diameters of ball bearings follow normal distribution, determine the following: (a) The probability of finding the diameter less than or equal to 4.05 in . (b) The probability of finding the diameter greater than or equal to 3.85 in . (c) The probability of finding the diameter between 3.9 in and 4.2 in , and (d) The central 98 th percentile probability limits of the diameter. (e) Find the value of x such that 12 % of the ball bearings have diameter less than x . 2. (20 points) A manufacturer states that the average lifetime of its light bulbs is 36 months, with a standard deviation of 10 months. Thirty bulbs are selected, and their
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