UNIVERSITY OF WINDSOR DEPARTMENT OF MATHEMATICS AND STATISTICS STAT 2910-02 - Test #1 Feb 16, 2022, 10.00 a.m. to 11.20 a.m. SURNAME, FIRST NAME LD. Marks - /80 Question 1: B Question 2: ns Question 3: 9 Question 4: 16 Question 5 : n2 Question 6: n2 Question 7: No Question 8: B Tol =i SC—SSCS1. A warehouse contains 6 computer printers, 4 of which are defective. A company randomly selects 3 of the 6 printers to purchase. Let the random variable & be the number of defective printers in the sample a) (3 marks), Write down the probability distribution of k. (1) ¢ ee) (é)(2.) (2) (4 ) nes b) (2 marks). What is the probability all 3 are non-defective? 4y( 2s) 4 G 6} else [ene = Zs 3 aay Ley) = GAGA RGR LTE Bt ©) (1 marks). What is the mean of 2? e n(4 = 3(4)- c d) (2 marks), What is the variance of x? - No oe (BU) Ge 4 : ale) “2 82. The following data represent the scores for a sample of 10 students on a 20-point chemistry quiz: 16, 14, 0, 8, 12, 12, 9, 10, 15, and 13. ne 10 at a) (12 marks). Find mean, median, Qi, Qs and the inter-quartile range and the sample variance. ee ah = ad 2 1064 in ib otdived tabas 0,8, 9, 1%, 1%, 1% 130% Uy Poscken of me se (nays rE (NS OS vosiMineh Qic 12eCD = ee ee) eo 7S Qc BHets(a-k ; a Ae? eqe(u) 7278 48 ost KIM Eabdgnarbl Cowge = O97 6) = 1H: 1s BPE =F He ete LL tak OMIA eh fipra - tor /e J ott) ec 4 4 self ze Mt irae (le) rie 7 iy gr sCieetdd 240 he b) (3 marks) Find the z-score for the smallest value in the data. Comment on whether this is an outlier with reason. 2 o-? ooh 2-297 . > : ty web an onttay as 18 2- Score 7-3 re ts3. Itwas estimated that on the average two cars pass through an intersection between 10 and 11 in the moming. Let x represent the number of cars passing through that intersection during this time. a) (2 marks). What is the probability distribution of x? ar a (A) aco cae eee a 2), b) (2 marks). What is the probability that only 2 cars have passed through that intersection? -2 2% -% (4) -2 2? 2 2 Be = 27) ne E = eae) — ©) @ marks). What is the probability that more than 7 cars passed through the intersection? p(ura) ale (xs 7)= PIBEF t-o98t = oral d) (1 marks). What is he mean of x? Mth e) (I marks). What is the variance of x? 6%e 2 4. (6 marks). Suppose that P(4) = 0.6, P(B) = 0.7, and that events A and B are independent. © (G7) 202 a. Find PUN) abarareu prareca)s (0) b. FingPdUB) 2 PAD 4 PUR) 90999) Se ueh gore (42 = o- Be ¢. Are the two events A and B mutually exclusive? Give reason. P(an ays PLA) PCB = Od #9, $0 fond & ave mot amu tually deel u sive 25. ‘An experiment can result in one or both of events 4 = Smoker and B= Female, with the joint probabilities shown in the table below. A person is selected at random. A Fats ec rams uy pranaleis ae [ois 0.10 erangy= 15, pcanale.) PAIS Fors SE POR 2644-355 FS a) (2 marks). Find the probability that the person is a smoker. ycare PL An Bra 7 And)es o-yorous 2 OSS b) (2 marks). Find the probability that the person is female. pays PC oan) +P( Pane 8404 OBS = OTS ©) (4 marks). Find the probability that the person is either a smoker or a female or both. FIRS CXC EE UL) ce sna) r 16S 475-040 G0 4) (4 marks). If the person is male, what is the probability she smokes? ) ome Pee pats vata )e 7 pane) . 1S 2 os play) ace) ie6. Let x denote the weight gain in pounds per month for a calf. The probability distribution of x is shown below. [x_T oe 0 O.1 5 0.3 10 A 1s 0.4 a) (8 marks), Find A. Find the mean and standard deviation of weight gain in pounds per month for a calf? As ie Gilddecu) = 0:2 Me Bx PIE ots BeteMy POX) = 2 TS ot ee 4x 90D ef upEe ag 22725 Gace (eagsope 12 b) (4 marks). What is P(x > 5| x < 15)? Show your work. 9 (¥73) x25) = v(xzs [x4 9) eC xa5 0 x +10) g(sda Pla) co Pike “plod PCS) 4 P (Ie) thar r ae a7. Suppose 40% of the TV sets in use in Canada on a particular night were tuned into game 7 of the Stanley Cup Playoffs. If we were to take a sample of 20 in-use TV sets that night, Let x be the random variable denoting the number of TV sets in use out of ‘the 20 sets samples. nro, P= oy a) (3 marks). What is the probability distribution of x? r0-K « praye(2e) ecm (FE UW) O47 weg bom b)(3 marks). What is the probability exactly three were tuned to the Stanley Cup Playofts? : ajay. 2 (ures? 2 10rg CAjveetly > MB)s fs pony =O-0I2 Vigne Oe #3) - Pix et) 2 oid Doog s Celle | ©) (3 marks), What is the probability 15 or more were tuned to the Stanley Cup Playoffs? Liye I- 0-986 = 71002 a aise 1 e(KE IDS I d)(2 marks). Find the mean and the variance of the number of in-use TV sets tuned to the Stanley Cup Playofis that night. Mmenp 22004) =8 eve we che) 2 TCM CHF wae8. A distribution of measurements is approximately mound shaped with mean 50 and sanded devise 10 ys SO, = 10 Gu ee MoD = ae 60) 1 (6-26, M420) = (Bo, 70) Ga72 (MSE, W43OD= (2 BP a) (2 marks) What percentage of the measurements will fall between 30 and 70? First draw diagram. Piveinbap of measurement bel” Zofee 3952 ) (2: marks) What percentage of the measurements will fall between 30 and 80? rc) 7 + "999 2 OGRE = ond D 47-257. ©) (2 marks) What might you say about a measurement 100? y= uo loo“ BO ow Bee = 7 luo bb an odd,