# hw3soln - ME 365 HOMEWORK SET 3 SOLUTION PROBLEM 1: Given:...

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ME 365 HOMEWORK SET 3 SOLUTION PROBLEM 1 : Given : 100 measurements with mean y 23 = and standard deviation S y = 1. Find : Fraction of readings you would expect between (a) 22 and 24? (b) 21 and 23? (c) 24 and 25? (d) Within what limits (equidistant on either side of the mean) would you expect to find 50% of the readings? Solution : (a) z = 1 table in Appendix A gives 68.27 % (b) z = 2 but only on one side ½ of 95.45 % = 47.735 % (c) let z 1 = 1 and z 2 = 2; we want ½P(z 2 ) – ½P(z 1 ) = ½(95.45 – 68.27) = 13.59 % (d) Interpolating the table for 50% gives z = 0.6745 22.3255 y 23.6745

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PROBLEM 2 : Given : 63 58 74 78 70 74 75 82 68 69 76 62 72 88 65 81 79 77 66 76 86 72 79 77 60 70 65 69 73 77 72 79 65 66 70 74 84 76 80 69 Find : (a) The standard deviation S t for the forty measurements. (b) The means 1 10 t ,. .., t of the four measurements in each of the ten columns; the standard deviation of the ten averages 1 10 .., t . Compare it to the standard deviation of the mean computed using the standard deviation of part (a). (c) Plot histograms for the forty individual measurements 1 40 .. , t , and for the ten means 1 10

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## This note was uploaded on 02/22/2012 for the course ME 365 taught by Professor Merkle during the Spring '07 term at Purdue University-West Lafayette.

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hw3soln - ME 365 HOMEWORK SET 3 SOLUTION PROBLEM 1: Given:...

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