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hw5soln

hw5soln - ME 365 Homework Set 5 Out September 22 2011 Due...

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ME 365 Homework Set 5 Out September 22 , 2011 Due September 29, 2011 Problem No. 1 Each member of a class of 50 students is given a piece of the same metal (or what is said to be the same metal) and told to find its density. From the 50 results the mean and the standard deviation are calculated. Given the following tabulation of the observed number of values within each internal, Bin k Values of in bin k Observations O k in bin k 1 Below 12 2 Between and 13 3 Between and 11 4 Above 14 (a) Determine 2 assuming a Gaussian distribution. Solution: Using table A of the appendix to chapter 4: The area under the normal distribution curve for the interval to is 68.27%. From this the probability for each interval can be determined: Bin 1 & Bin 4: P 1 P 4 1 0.6827 2 0.15865 Bin 2 & Bin 3: P 2 P 3 0.6827 2 0.34135 Multiplying each probability by the total number of measurements, 50, the expected number of values in each bin is determined and the following table can be constructed. Bin k Values of in bin Observations O k Expected E k O k E k 2 E k 1 Below 12 7.9325 2.085667 2 Between and 13 17.0675 0.969360 3 Between and 11 17.0675 2.156998 4 Above 14 7.9325 4.640978 2 9.853003 (b) State your reasons for either accepting or rejecting the Gaussian hypothesis.

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