Final Exam with Answer Key - Probability and Statistics Engineering | STT 351, Exams of Probability and Statistics

Download Final Exam with Answer Key - Probability and Statistics Engineering | STT 351 and more Exams Probability and Statistics in PDF only on Docsity! final002.nb 1 STT351-002 Final Exam 1-2. TREE. 20% of fields are productive. Pr 85% of productive fields appear productive A gS PA 12 (: 45) 5% of non-productive fields appear productive. Make a tree. PA +8 (98) PeAC CH) 1. P(ficld appears productive) Pi = KPA) KPA) = 2 (89) + 805) 2. P(field is productive | field appears productive) = (CF Us PA) = 2ED/ C2 (aS). 6¢25)) 3-4. CI and TEST for MEAN 4. le of n = 6 prescription eyeglass lenses is is drawn from a process under statistical contro). Each of these six is subjected to mea- surements which determine an over Xx = “conformity to prescription." The sam- ple mean = 2.2 and the sample sd s = 2.8. é pene 3. Determine the 95% Clforp. + £ 3 Lom PF Ft prsé-]=S- PESTS s ia aS? | 4. Determine the final sample size AFIN AL required for 95% hybrid Cl Xa, + 0.04 Mit _ Z, burt ae = OY We ANC. ji- nN = (ba tat) = ZSH 008 idiceeesio final002.nb 2 5-6. Probability Rules. P(A) = 0.6, P(B) = 0.9, events A, B are independent. 7-8. Drawing balls. Draws will be made without replacement and with equal probabil- ity on those remaining from {R R R Y Y B BB B} (ie. 3R, 2 Y, and 4 B}. 7. P(R4) = + by what simple principle? gepee, a DEAL oes NP MAPPER PRED = ECL) = X% 8. Use rules of probability to PROVE P(R2) = by breaking down event R2 accord- ing to what happens on draw one. Cite the rules you use. PCRL) = PRI RL) + PCRICR 1) Tora reek =*&) FRR) Y Pope) Page d al, 4a 9-10. Estimates. A Fhe of n= P10 a Ba thon Soka cement and with equal probability from a population of size 300. This sample has mean X = 2.1 with s = 0.6. 9. Estimate the sd o-y of sample mean ¥ a Aiour KG 1 A _ | Ber feo. 2,6. W-? UR Bea} ap 10. Estimate the margin of error for X. ip G6 Tomes @ Dé 19S i Bas-/ [756 final002.nb 5 21. Kernel density. Beli curves are placed at each of two points (see below). Plot the kemel] density estimate. Take care to do it correctly (show five pts accurately). 10 12 18 22-24. Rules for E, Var, sd. Random variables X, Y are independent with EX=6 Var X=4 EY=9 Var Y=2 22. E(XY) “2 EX EY = & @) 23. E(Y?) (follows from Var Y=E (Y2)-(EYY) = Ytr—y” = Q pas me tora N 5 2227) = lax(x-0y) slo O Mo = VacQn 4p 40? final002.nb 6 23. Plot regression line. Parts are sampled with-replacement and scored (x, y) where x = serial number of part y = hardness. The sample data are: : X = 1343 Sy = 433 m= 200 pairs (x, y} y= 127 Sysllo r=07 What is the value y for a point on the regression line with x = 1343 + 433 (i.e. one sam- ' ple sd above the sample mean in the x-scale)? ANS - § 724 = LP t+ OPEL) 26. Proportionally stratified. A population of motors is stratified by supplier 20% A 10% B 10% C A stratified sample of motors produces the following sample means by stratum stratum A B Cc sample mean 2.4 2.7 2.0 Estimate the population mean p from the above data. Ka Saks = .200) 4 MZD+ Ie c=} 27. Calculating-SD. For the following discrete distribution calculate the standard devia- tion’, x Pa) x Poy x” P6x) Q 08 a oO I 0.2 2b a EARL eared ir Vek = VEXED = Yao 2-8 4 USdAL FeaRMVER UPep Fee EY) STOKES Final002.nb 28-29, Multiple regression. A random sample of 400 of our products is selected from. stores nationwide. Each is scored for y = selling price x1 = 1 if store is major retailer, 0 if not x2 = quantity ordered by store A multiple linear regression is fit to this data resulting in the fitted model y = 44,75 - 7.80 x1 - 0.083 x2 28. Determine the average effect on price (according to the fitted model} occa- sioned by adding 500 to the order and switching from a major retailer to one that is not a major retailer. & 7. & C FRom - 804 fo -7.89 ©)) - 9,083 (S29) (Fem — 0, 083% Te ~- O83 Gar foe) Ay = 78 — @ C8 PSez) wer 29. Compare the 95% CI of yz based on J = 42.76 with that based on the regres- sion based estimator if £ CORRECTION sample multiple correlation is R= 06, tegression based estimator works out to 37. 80. 25% CTosing Y £ ic Be nn 196 be 95% CI using regression based estimator 37 go4 Ie LE oa Vnosté-s ) 30. t-TEST. A process is in control. Each part produced is score-x = finishing time. A sample of 12 will be used to monitor the process in a test of the null hypothesis A: py, = 5 (minutes) vs Hy: #5 witha =O.1 RSID aya aud, OS ate 30. If the test statistic for a sample of 12 evaluates to t = 2.8 what action is taken by the test? Indicate your reasoning. DF = m-l = /l-/ =//- Ks = Oe Kev? Ag iF | tesp7AT / > tego Ca. \ t SIL wi HF 12,8[> 1796 - le oe ee ee <a ON ob rab SALT > 2-8) = = & (07 A) ts , Ue ee et