351HW Sols

# 351HW Sols - 351-Prob& Statisitcs for EngineersSolutions...

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Unformatted text preview: 351-Prob. & Statisitcs for EngineersSolutions for Even-Numbered ProblemsChapter 2Section 2.1 :2, 4, 6, 9, 102 (a) The sample mean is x= (100.4/8) = 12.55.The sample size (n = 8) is even. Therefore, the sample median is the average of the (n/2) and (n/2) + 1 values. By sorting the 8 values in order, from smallest to largest: 8.0 8.9 11.0 12.0 13.0 14.5 15.0 18.0, the forth and fifth values are 12 and 13. The sample median is (12.0 + 13.0)/2 = 12.5.The 12.5% trimmed mean requires that we first trim (.125)(n) or 1 value from the ends of the ordered data set. Then we average the remaining 6 values. The 12.5% trimmed mean )5.12(trxis 74.4/6 = 12.4.All three measures of center are similar, indicating little skewness to the data set.(b) The smallest value (8.0) could be increased to any number below 12.0 (a change of less than 4.0) without affecting the value of the sample median.(c) The values obtained in part (a) can be used directly. For example, the sample mean of 12.55 psi could be re-expressed as (12.55 psi) xksi70.5psi2.2ksi1=.4.The three quantities of interest are:.and,,11++nnnxxxTheir relationship is as follows:++=++=++=+=++=++=+∑∑11111111111111nxxnxxnnxxnxnxnnnnnininiinFor the strength observations, 34.4310=xand 5.8111=x. Therefore, 81.461105.81)34.43)(10(11=++=x110.+=-=-=∫21212ababxdxabxbabaμSection 2.2 : 18, 23, 24, 26, 27.18.The sample mean, (292.116162,11011===∑ixnx.The sample standard deviation, (29(2975.25910162,1992,1401222=-=--=∑∑nnxxsiiOn average, we would expect a fracture strength of 116.2. In general, the size of a typical deviation from the sample mean (116.2) is about 25.75. Some observations may deviate from 116.2 by more than this and some by less.26.Extending the result from exercise 25, we know:(29∫∫∞∞-∞∞--=-=2222)()(μμσdxxfxdxxfxSo, in the case of a uniform from a to b,23222311μμσ--=--=∫babaxabdxabx(29(29233233413112331baababbaabab+---=+---=(29(29(2922221214131abbababa-=+-++=For the task completion time application, a = 4 and b = 6.52642=+=+=baμ(29(2931124612222=-=-=abσ(29(29(29(29315315-〈++〉=-〈++〉xPxPxPxPσμσμ2(29(29423.21152115.24423.42577.56423.4577.5=+=-+-=〈+〉=xPxPSection 2.3 : 35, 37, 42, 4342.X= fracture strength of silicon nitride braze joints. X follows a Weibull distribution with 1255==βα(a) The lower quartile of X: (295125125....
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351HW Sols - 351-Prob& Statisitcs for EngineersSolutions...

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