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Solutions Exam 2 Review

# Solutions Exam 2 Review - W9 Luna 5 “he mndom mu{Ly-mk I...

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Unformatted text preview: W9 Luna} 5 “he mndom mu. ? {Ly-mk- I: appc‘bpr.‘ck_ . - 9 1. In a statistics class with 15 males and 13 females, 5 students are selected to put d" “‘me ‘ problems on the board. my dc. but Mud om.“- WV dd." ? outﬂow“: 3 Review for Exam 2 a. What is the probability that of the 5 selected 3 are females? N = 28' 5= Fag-=5) =( C 3W 02) = 0.3% ﬂ -.-: 5:, x = 3 2': as b. What is the probability that of the 5 selected 2 are males? N=21r P(><;,=2) ‘-‘ (“C2 {act} = 0.3% S = IS '——‘—_____—' n -.-.- S' ZYC s- X = Q c. What is the probability that of the 5 selected 2 are males and 3 are females? — .- 7 ¥ Shhmc-l Can I Quad b3 PCX; —3)PC mez) . no nu t “he, Fur-=3 ma Xm=2) = P(>(F=’3) PCXm=2 l xpca) Ofaou - :L = 0%0ko d. What is the probability that the group of students selected has either 3 females or 2 males? Foot-:3 or xmsz')= PCX;=%) .— P(Xm=2) " P(Xp=3- W Xm32) 7:. GHQ-{3L9 + Urbblﬂ ~O.30{0 “= 0.30% I~/ 2. Customers use an automatic teller machine at an average rate of7 per hour. a. What is the probability that exactly 10 people will use the ATM in the nexthour? l0 _ N‘W ch-no)‘: (—0 e, 1 x 00‘qu8 )(IIO IOL Cf lmu up on graph b. What is the probability that 12 or more people will use the ATM in the next hour? + 0.0002 '1' O DOD1 '3 0-03—52 c. What is the probability that less than 6 people will use the ATM in the next hour? PCxLo) -—- {900:0 -: may m PfX’DcS‘) 0(99 * 00223 .= 0.0009 + 00 + Obszl * 0.09:2 +0427"! 1“ 0.30mi: A statistics instructor collected data on the time it takes the students to complete a test. The students take anywhere between 35 minutes and 55 minutes. There is an equally likely chance that students will take 35 minutes as it is they will take 55 minutes. a. How long does the typical test take? -..-: PCX‘: It!) . PCX 3 v2} = chziz) +ch 13) *r = 0.02033 + O. omz + OVOO'II + 0.0033 + (3.0th v 0.0009 b. What is the probability a particular student will take 45 minutes? ﬁx =q8’) = POMS g xeqsx) .__‘__(qs.sr-W.r) = 0.08' 55— 35' 'll c. What is the probability a particular student will take less than 45 minutes? Ptxau§3= l (qr—35") —— 0.3" (Sf-35' 4. Captain D’s tuna is sold in cans that have a net weight of8 ounces. The weights are normally distributed with a mean of 8.025 ounces and a standard deviation of 0.125 ounces. You take a sample of 36 cans. a. What is the probability that the mean is greater than 8.03 ounces? i. What is the sampling error? N ”-02? 32—14 —= \$03 — \$22025" = 0.003- 10 = 8b ii. What is the standard error? <3“ 0.12s“ =. 2: 0.0 O J77 dam 2 S) b. What is the probability that the mean ofthe sample is between 7.995 and 8.03? Ere 90'5— <z.025‘ : 0.2.1 =~> %; PCOéZé orzq) =00qu OJZf/Jﬁb ‘22 = 199\$- f‘Z‘OZ‘T 1:. -—I.<-1Ll 1:) PGqu-e 1'3 (:0) = 0-42§l Oar/JET 90%: e. 3? egos) -—- 00°!“ 3 + OM’ZSI = 035‘qu 5. It is very difficult for small businesses to be successful. The Small Business Administration estimates that 20 percent will dissolve or go bankrupt within two years. A sample of 50 new businesses is selected. a. What is the probability that exactly 14 will go bankrupt? -N “=50 P(x—1q)=CM(O.H® 0—0502] "W : 0.2 5° = O. @4961 a. ‘h b. What is the probability that between 7 and 9 businesses will go bankrupt? I l 9074- >619) = WT) * “‘33 * em) '7 q 03 3b 01" L U" 3/. Mzn'nz'b'oCOQ) — “(paﬁfpé g 0‘“:- n-nCI-ﬂ ngoOcomco?) 9'?3 4‘7 ‘1 o 4 pm, «140) 0C)! '2‘ =<_[—O.S-)—IO = "l.’231 =9 "30-3ng 9.?3 6. Other important topics: _ (q + 0 8-3- [0 122 "' ' “:- "' 0.171 a. Definitions from chapter 5 ‘2 .2’ 3 b. Why do we sample? =9 {DC—OA‘I'I‘E‘ 0) 0.0114 c. Characteristics ofall probability distributions P(7§:X£’Q)= O 30.25“ -0.G‘UH d. Characteristics of binomial, Poisson, hypergeometric, uniform, and normal , "I O . '32.” e. Types of sampling f. Probability views g. Central limit theorem ...
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