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# 173 Note 6 for M E 345 with Professor Cimbala at PSU

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Date Created: 02/06/15

ME345 Fall 2009 Professor John M Cimbala Today we will Do some review example problems The Gaussian PDF Review the pdf module The Central Limit Theorem CLT Do some example problems CLT Review the first half of the pdf module Other PDFs the Student s t PDF De some exarrrplepro olemmtttdent W r WT 0quot quot13949 Example Review and probability Given The temperature of an ice bath is measured numerous times with a digital thermometer The true temperature of the ice bath is 0000000 The sample mean temperature is T 00125 C The sample standard deviation of all the readings is 003410C i S We assume that the errors in the readings are purely random 2 a To do Write T in standard engineering format T 00125 i 0H 0C b To do Calculate the bias error also called systematic error c To do Calculate the probability that any random reading is greater than 0 C Solution 0 8w t c quot 1 moral HT Z 39quotl 2 xW 9 3 39 39 Milt1 7 Squot 003 11 H AGFDM quot ow fab O39S Am WTgt 03963 39 S39om a 53m 3W4 Example Probability power requirement measurements Given Bev takes 2l measurements of the power requirement for an electronic instrument running in a steadystate mode We assume that the errors are purely random The sample mean is 3592 W and the sample standard deviation is 060 W To do a Considering the proper number of significant digits show how Bev should write the power in standard engineering format 95 confidence level ie P3592 i W 5 b Calculate the percentage of the readings that are expected to be less than 3592 W c Calculate the percentage of the readings that are expected to be greater than 3712 W d Estimate the number of readings that are expected to be greater than 3712 W Solutlon 19 31114 3931 HA Z 5 9 v 060 Kt Am m wad 539 Liv 1amp1 Ayfumilx I l 2 t 5940 3 Q 39 1 NM 2 04111 A Aw Uquot 00quot 0917 03773r Ear Ema Q La 0mm my 2 le o 35 M11512 dl 2 our Clea g Weenle 9amp0quot Y MSWquot N mquot 5 W on M 0oe3auk um gum v 1 ml luaug Squot A39 Q homr a fu J39mu M l but fake or 60cu5 nrf Ramses mm 357 mama was Q Example Estimating population standard deviation Given A company produces resistors by the thousands and Mark is in charge of quality control 0 He picks A resistors at random as sample 1 and calculates the mean f1 0 He picks 20 other resistors as sample 2 and calculates the mean f 0 Mark continues to do this until sample 25 and calculates the mean 25 The average of all the means is 1 2 2525 8235 kQ The standard deviation of all the means is 0397 m S7 0282 kQ To do Estimate the population standard deviation 039 Solution Uh H n 1 0 N 75 at thk 51 4 S Sow 7 CcszS V x a 6 6 0131 H W AC Lu m 8 viwk r pquh nu39 639 Example Estimating population standard deviation Given Ron takes 50 pressure measurements and repeats this 19 more times for a total of 20 samples of 50 data points each He calculates the sample mean for each set sample of 50 measurements The standard deviation of the 20 sample means is 0150 kPalt S To do Estimate the population standard deviation of all the measurements in units of kPa to 3 Slgmflcant d1g1ts Solution U Clxr Guam Lvlwil ltersquot 7 T O 6 C Squot I a CLT5C 67 T So cf mflz Ni ii J Mf lquot QSKY39 G oasMASE 10L m

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