MTH 345 Exam 2 Review Questions Fall Based on a Bellowes survey of adults, there is a 0.48 probability that a randomly selected adult uses a

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1 MTH 345 Exam 2 Review Questios Fall Based o a Bellowes survey of adults, there is a 0.48 probability that a radomly selected adult uses a tax preparer to file taxes. Fid the probability that amog 15 radomly selected adults, exactly 9 use tax preparers to file their taxes. 2. The math portio of the ACT test cosists of multiple-choice questios, each with five possible aswers (a, b, c, d, e), oe of which is correct. Assume that radom guesses are made for six questios. Fid the probability that the umber of correct aswers is at most Based o a Harris poll of 370 adults who regret gettig tattoos, 20% say that they were too youg whe they got their tattoos. (a) For radomly selected groups of 370 adults who regret gettig tattoos, fid the mea ad stadard deviatio for the umber who say that they were too youg whe they got their tattoos. (b) For a radomly selected group of 370 adults who regret gettig tattoos, would 84 be a uusually low or high umber who say that they were too youg whe they got their tattoos? Explai. 4. Assume that for a recet 42-year period i Coutry X, there were 147 earthquakes measured at the 6.0 or higher o the Richter scale. (a) Fid the mea umber of earthquakes per year. (b) Fid the probability that i a give year, there are exactly three earthquakes i Coutry X that measure 6.0 or higher o the Richter scale. 5. (z scores) Assume that scores o a test are ormally distributed with a mea of 0 ad a stadard deviatio of 1. Fid the probability of the give scores. (a) Greater tha 0.72 (b) Less tha 2.34 (c) Betwee 0.35 ad 1.35 (d) Greater tha (z scores) Assume that scores o a test are ormally distributed with a mea of 0 ad a stadard deviatio of 1. Fid P 27, the 27th percetile. This is the score separatig the bottom 27% from the top 73%. 7. The otatio z is used to represet the z score with a area of to its right. Fid the value of z Wome s heights are ormally distributed with mea 63.6 i. ad stadard deviatio 2.5 i. A Tall Club has a membership requiremet that wome must be at least 68.5 i. tall. What percetage of wome meet that requiremet? 9. Assume that SAT scores are omally distributed with mea 1518 ad stadard deviatio 325. If 18 SAT scores are radomly selected, fid the probability that they have a mea betwee 1430 ad Birth weights i Norway are ormally distributed with a mea of 3570 g ad a stadard deviatio of 500 g. What is the percetage of ewbor babies weighig betwee 3280 g ad 3450 g? 11. Assume that adults have IQ scores that are omally distributed with mea 100 ad stadard deviatio 15. Fid P 24, which is the IQ score separatig the bottom 24% from the top 76%. 12. A airlier carries 80 passegers ad has doors with a height of 70 i. Heights of me are ormally distributed with a mea of 69.0 i. ad a stadard deviatio of 2.8 i. If half of the 80 passegers are me, fid the probability that the mea height of the 40 me is less tha 70 i. 1

2 13. I each of parts (a) ad (b), assume we wat to costruct a cofidece iterval usig the give cofidece level. Choose ad do oly oe of these three choices, whichever is appropriate. If the ormal distributio should be used, the fid the critical value z α/2. If the t distributio should be used, the fid the critical value t α/2. If either the ormal or the t distributio applies, the state this. (a) 95%; = 12; σ is ukow; populatio appears to be very skewed. (b) 90%; = 9; σ is ukow; populatio appears to be ormally distributed. 14. Twelve differet video games showig substace use were observed ad the duratio times of game play (i secods) are listed below (based o data from Cotet ad Ratigs of Tee-Rated Video Games, by Haiger ad Thompso, Joural of the America Medical Associatio, Vol. 291, No. 7). The desig of the study justifies the assumptio that the sample ca be treated as a simple radom sample, ad assume that the populatio has a ormal distributio. Use the sample data to costruct a 90% cofidece iterval estimate of the mea duratio time of game play for the populatio Usig a simple radom sample of weights of Aimal A, we obtai these sample statistics: =40adx = lb. Research from other sources suggests that the populatio of weights of Aimal A is ormally distributed ad has a stadard deviatio give by σ =30.86 lb. Costruct a 90% cofidece iterval of the mea weight of all Aimals A. 16. Assume you must coduct a poll to determie the percetage of adults who believe that it is morally wrog ot to report all icome o tax returs. How may radomly selected adults must you survey if you wat 99% cofidece that the margi of error is two percetage poits? Assume that othig is kow about the percetage that you are tryig to estimate. 17. Whe Medel coducted his famous geetics experimets with peas, oe sample of offsprig cosisted of 580 peas, ad it was observed that 152 of them were yellow. Fid a 99% cofidece iterval estimate of the percetage of yellow peas. 18. I each of parts (a), (b), ad (c), assume we wat to costruct a cofidece iterval usig the give cofidece level. Choose ad do oly oe of these three choices, whichever is appropriate. If the ormal distributio should be used, the fid the critical value z α/2. If the t distributio should be used, the fid the critical value t α/2. If either the ormal or the t distributio applies, the state this. (a) 99%; = 10; σ = 15; populatio appears to be ormally distributed. (b) 90%; = 6; σ is ukow; populatio appears to be ormally distributed. (c) 80%; = 32; σ is kow; populatio appears to be ormally distributed. 19. As a maufacturer of golf equipmet, the Spaldig Corporatio wats to estimate the proportio of golfers who are left-haded. (The compay ca use this iformatio i plaig for the umber of right-haded ad left-haded sets of golf clubs to make.) A previous study study suggests that 15% of golfers are left-haded. How may golfers must be surveyed if we wat 98% cofidece that the sample proportio has a margi of error of 2 percetage poits? 20. The serum cholesterol levels i me aged 18 to 24 are ormally distributed with a mea of ad a stadard deviatio of The uits are i mg/100 ml, ad the data are based o the Natioal Health Survey. A Health Maiteace Orgaizatio wats to establish a criterio for recommedig dietary chages if cholesterol levels are i the top 7%. What is the cutoff for me aged 18 to 24? 21. Whe people smoke, the icotie they absorb is coverted to cotiie, which ca be measured. A sample of 32 smokers has a mea cotiie level of Assumig that σ is kow to be 119.5, fid a 99% cofidece iterval estimate of the mea cotiie level of all smokers. 2

3 22. A study was made of seat-belt use amog childre who were ivolved i car crashes that caused them to be hospitalized. It was foud that childre ot wearig ay restraits had hospital stays with a mea of 7.37 days ad a stadard deviatio of 0.79 days (based o data from Morbidity Amog Pediatric Motor Vehicle Crash Victims: The Effectiveess of Seat Belts, by Osberg ad Di Scala, America Joural of Public Health, Vol. 82, No. 3). If 40 such childre are radomly selected, fid the probability that their mea hospital stay is greater tha 7.25 days. 23. I a study of the use of hyposis to relieve pai, sesory ratigs were measured for 16 subjects, with the results give below (based o data from A Aalysis of Factors That Cotribute to the Efficacy of Hypotic Aalgesia, by Price ad Barber, Joral of Abormal Psychology, Vol. 96, No. 1.) Assume the populatio has a ormal distributio. Use these sample data to costruct the 95% cofidece iterval for the mea sesory ratig for the populatio from which the sample was draw With destructive testig, sample items are destroyed i the process of testig them. Crash testig of cars is oe very expesive example of destructive testig. Let s assume that you have crash tested twelve Dodge Viper sports cars (list price: $59,300) uder a variety of coditios that simulate typical collisios. Aalysis of the twelve damaged cars results i repair costs havig a distributio that appears to be bell-shaped, with a mea of $26,227 ad a stadard deviatio of $15,873 (based o data from the Highway Loss Data Istitute). Assume that the sample is a simple radom sample obtaied from a populatio with a ormal distributio. Fid the 90% cofidece iterval estimate of the stadard deviatio of repair costs for all Dodge Vipers ivolved i collisios. 25. Fid the critical values (a) χ 2 L ad (b) χ2 R that correspod to the give degree of cofidece ad sample size. (Clearly ote which is (a) ad which is (b).) 99%, = The listed values are waitig times (i miutes) of customers at the Bak of Providece, where customers may eter oe of three differect lies that have formed at three differet teller widows. (Assume that a simple radom sample is selected from a ormally distributed populatio.) Costruct a 95% cofidece iterval for the populatio stadard deviatio σ Examie the give statemet. Put this claim i symbolic form. The write dow the competig idea i symbolic form (i.e., give the symbolic form that must be true whe the give claim is false). The write dow the ull hypothesis H 0 ad the alterative hypothesis H 1 i symbolicform.besuretousethecorrectsymbol(μ, p, σ) ieachaswer. Claim: The proportio of households with telephoes is greater tha Origial claim i symbolic form: 2. Competig idea i symbolic form: 3. H 0 : H 1 : 28. Examie the give statemet. Put this claim i symbolic form. The write dow the competig idea i symbolic form (i.e., give the symbolic form that must be true whe the give claim is false). The write dow the ull hypothesis H 0 ad the alterative hypothesis H 1 i symbolicform.besuretousethecorrectsymbol(μ, p, σ) ieachaswer. Claim: The mea pulse rate (i beats per miute) of adults is 76 or lower. 1. Origial claim i symbolic form: 2. Competig idea i symbolic form: 3. H 0 : H 1 : 3

4 Aswers: (a) μ = 74, σ =7.69 (b) No, because umbers betwee 58.6 ad 89.4 are ordiary. 4. (a) 3.5 (b) (a) (b) (c) (d) % (tech ) % (a) Neither z or t (b) t α/2 = <μ< <μ< <p< (a) z α/2 =2.575 (b) t α/2 =2.015 (c) z α/2 = (tech ) <μ< (tech ) <μ< <σ< (a) χ 2 L = <σ<3.33 (b) χ2 R = p > p H 0 : p =0.35 H 1 : p> μ μ > H 0 : μ =76 H 1 : μ>76 4

5 Formulas for Exam 2 Ch 5: Probability Distributios! P (x) = ( x)! x! px q x = C x p x q x Biomial probability μ = p Mea (biomial) σ 2 = p q Variace (biomial) σ = p q Stadard deviatio (biomial) P (x) = μx e μ Poisso Distributio where e x! (For Poisso, σ = μ.) Ch 6: Normal Distributio z = x x or x μ Stadard score s σ x = μ + z σ μ x = μ Cetral limit theorem σ x = σ Cetral limit theorem (Stadard error) z = x μ (σ/ Cetral limit theorem ) TI-84 Commads biompdf(, p, x) poissopdf(μ, x) ormalcdf(l, R, μ, σ) ivnorm(a L,μ,σ) Ch 7: Cofidece Itervals (oe populatio) ˆp E<p<ˆp + E Proportio ˆpˆq where E = z α/2 1-PropZIt x E<μ<x + E Mea s where E = t α/2 (σ ukow, see flowchart) TIterval or E = z α/2 σ (σ kow, see flowchart) ZIterval ( 1)s 2 <σ 2 ( 1)s2 < Variace χ 2 R ( 1)s 2 χ 2 R <σ< χ 2 L ( 1)s 2 χ 2 L Stadard Deviatio Ch.7: SampleSizeDetermiatio = [z α/2] E 2 Proportio (ˆp ad ˆq are ukow) = [z α/2] 2 ˆpˆq E 2 Proportio (ˆp ad ˆq are kow) [ zα/2 σ ] 2 = Mea E 5