Introduction to Statistics - Practice with Solved Test 2 | STAT 1222, Study notes of Statistics

Download Introduction to Statistics - Practice with Solved Test 2 | STAT 1222 and more Study notes Statistics in PDF only on Docsity! stat 1222 TEST 2 Review Sole fom Hidley 1. Review all relevant quizzes and homeworks. 2. The probability distribution of a random variable x is as follows: 2 [ij2,;s)4 [5 la Pay | at eta 123 138 : zu (a) Find the missing probability. | — (sp4-p4-e54-¢¢) =17-@2-2 =P lxe2z) (b) Find the expected value and the standard deviation of the random variable 2. (c) Find P(x <2orz2>4). = Pleen +Plxez2)9 +P Os ys . i “lez 78S 3. Find the z-scores that has ag E65 “> ’ (a) 98.5% of the distribution’s area to the right. > 0% *s- a) -.33b) .33(c)}-2.17 d) 2.17 e) 0.0 bo UF (b) 95.4% of the distribution’s area between —z and z. a) ~1.645 and 1.645 b) -1.28 and 1.28 ¢) -1.96 and 1.96 (a)) -2 and2 e) -2.875 and 2.575 sh outs: 4, Find the following normal probabilities for the given parameters, Se) 023 elm ary (a) w=5,0=0.2, P(S<2< 5.64) z = 04g a) 95 b) 9993 c) 05 a) 4993 e) 1 ~2 Ze (b) w= 18.5,0 = 9.25, P(e <0 or 2 > 37). 023 “ 2-0 a) .0228 b) .5228 c) .9772 d) .9544 e) .0456 -2-0 (c) # = 50,0 = 100. A random sample of size 100 is drawn. Find the probability that the sample mean Z exceeds 75. 5. In a recent year, the ACT scores for high school students with a 3.50 to 4,00 grade point average were normally distributed, with a mean of 24.2 and a standard deviation of 4.2. (a) Tf a state university automatically admits the top 7%,of students, what is the least score that a student can receive and still be admitted Mugg mart ca My? (b) In this same university, a student becomes ineligible for admission if he/she scores in the bottom 12%. What is the minimum score that a student needs to be eligible for admission? (c) Find the probability that a randomly chosen high school student has an ACT score between 20 and 28.4, (d) Ifa sample of 25 students are randomly selected, find the probability that the average score of these students lie between 20 and 28.4. P(zoa® 4 2Gely ) (e) If 150 students are randomly selected, how many will have an ACT score that is more than 28.4 ? (f) What score represents the first quartile? 6. Section 5.3: page 244, # 45 7. The per month rent of houses in a city are normally distributed: with mean rent of $5000 and standard deviation of $300. A random sample of 15 houses is selected. {a) Identify the mean and standard error of the mean rent of the random sample of 15 houses. a) 5000, 300 b) 5000, 20 c) 5000, 77.46 d) 333.8333, 20 e) 333.3333, 77.46 (b) What is the probability that the mean rent is greater than 52007 a) 8413 b) 1587 ~—c) 0049 =~ d) «9974 —e)-«.0026,  0 hebrew fo View | xe (Lx xf Plry 2b ass S02 | oe gerozs “hss \2-yors |e ag a5 ee OF *302¢ g2dre "GS \ Lots | ros og ese rte le Gs | gstoese \ °F 3s87s- Be 5S \ ° ST Le Fx Pl) 4 \ \! 14% 2. 2 nM = expected value : ~~ 2 lems Pie) = 4G es oe hens SH bv o> (rae ZL Ye o~ ff) Me 2he2 - OR a gfuante j a je ear hebe Slept for be "f an Poe Pfulrbce, ZO < Rey an 2 i bP G2) (6) ee] he AA wet AA piven pn He beak . (4) Prod om Aumpilyy ste babi. Me S000, X= 300 His, Los - = = Boo Aw (e) Mg = Mer Sip ase fe: 22 MM a Sw. = 4 pgStT ee wMede PCa > SS ): He > bes) ” ite Shavciedl ation Ns 21> wes bf f 2-286 : for K co) 449) = % 25% Pow Pout Ce) _ 99951 (6x Cd- fo My Metis y ange a ample. = n4 bf > Xt BK Ts ~ ~ KD te okr tA X~ FOO, 4: 750, Ur rT Berriz 7 Ca o 1s ve! 2 Ot oud side [992-08 CJ> $004 wz wee ee [ each w= 298 2601S J = E00 + AGS ves a “si? wily vse (tv) (9) neg” frond aa owpley A unknown, Hyena ppb, fe Use te Ol: xt he X= $0, 5214, dfzic-tety } CT ® bt pHrth - i Weis, Re c=t0't., PHI Ye Bot fr 35s = [13-6344 , Bb» 36%) “ H _ § (€) ($b) Within 44 | a gen C2471, fe = 219 [rw ga shoe) MO USB NS prainge ye Be 1e88 2 Hg af ere tow) B.1, PoV2, Ch, B= febas We [1chibe be 2 i Je Se S467 2 oF @ 2 L045. we Steere j “To fo Fax 7p re) Fant chy cr44),. 1 fe 74 - fs Loxgen hour ce vo % becaure the Lorre frowsing 2e is Lupe 2 a ) ~% % a ye po pullin Wer ugl ve. é . 2 B= 20, he ¥, af F-1 26 CH 987. CL + e000 4 P12 220 . Aws:- (iv) AR = WoW t 13-45°¢¢ toh) Cray, th) urd, & Wh nrown, tb X= '100+00 Le > 32/43, ~ (Pb 2912, 129. ieee) = pe Hid svhtion, @ eV of ho prior infeemotchon avalible, Un, I- ©, £ = 70, ¢-49th, B22 995° 9 (2 )%= Cos; (5)/ REPENS 59G- es "08 ~ [ES FE