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# Final Exam Review Questions Solutions Guide

- From Mathematics, Data Analysis

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**Review Questions**

**Solutions Guide**

**You may want toPRINT THIS so you can carefully check your answers. Be sure toask your instructor if you have questions about any of the solutions given below.**

**1. **Determine if each of the following represents nominal, ordinal, interval, or ratio data.

a. Movie ratings

b. Test scores

c. Colors of shirts

**2. **Thefollowing numbersrepresenttheweights in poundsofsix 7- yearold childrenin Mrs.Jones'2ndgradeclass.

{25,60,51,47,49,45}

Findthemean;median;mode;range;variance;standard deviation.

**3. **Ifthevarianceis846,whatis thestandarddeviation?

**4. **Ifwe havethefollowing data

34,38,22,21,29,37,40,41,22,20,49,47,20,31,34,66

Drawastemandleaf.Discusstheshapeofthedistribution.

**5.**What type of sampling technique is (a) a wheat field is divided into sections and a random sample of stocks are taken from each section, and (b) a manufacturer measures every 80^{th} bottle to test for quality?

**6.**If a data set with a normal distribution has a mean of 32 and a standard deviation of 4.9, what percent of the data would you expect to find between 27.1 and 36.9? What range encompasses 99.7% of these data?

**7. **Determine the regression equation for the following data:

X: 4 5 7 3 2 7 8 9 7 6 4 6 5 9 3 2 1

Y: 9 7 8 6 9 5 6 4 3 6 7 8 9 3 4 2 4

**8.**If the correlation coefficient is -.749, what would be the value of the coefficient of determination?

** **

**9. **To predict theannualriceyield in poundsweusetheequation

*y*ˆ=859+5.76*x*1+3.82*x*2,wherex1representsthenumberofacres plantedandwherex2representsthenumberofacres harvestedandwherer2= .94.

a) Predicttheannualyield when3200acresareplantedand3000 areharvested.

b) Interprettheresultsofthis r2value.

**10. **TheStudentServicesofficedidasurveyof500studentsin which theyaskedifthestudentis part-timeorfull-time.Anotherquestion askedwhetherthestudentwasatransferstudent.Theresultsfollow.

TransferNon-Transfer Row Totals

Part-Time

100

110

210

Full-Time

170

120

290

Totals

270

230

500

**a) **Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis atransferstudent.P (Transfer)

**b) **Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis aparttimestudent. P (PartTime)

**c)**Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis atransferstudent andaparttimestudent.P(transferANDparttime).

**d)**Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis atransferstudentif we knowheis aparttimestudent.P(transfer| parttime).

**e)**Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis aparttimegivenhe is atransferstudent.P(parttime| transfer)

**f****)**Aretheeventsparttimeandtransferindependent?Explain mathematically.

**g)**Aretheeventsparttimeandtransfermutuallyexclusive.Explain mathematically.

**11. **Ashipmentof40televisionsetscontains3defectiveunits.How manywayscanavendingcompanycanbuyfiveoftheseunits and receivenodefectiveunits?

**12. **In the US, 28% of people consider snickerdoodle as their favorite cookie. You asked 5 people if their favorite cookie was snickerdoodle. Create the probability distribution for the possible outcomes.

**13. **TherandomvariableX representstheannualsalariesin dollars of agroupofteachers.FindtheexpectedvalueE(X).

X = {$35,000;$45,000;$55,000} where,

P(35,000)= .4;P(45,000)= .3;P(55,000)= .3.

**14. **Anadvertisingagencyis hiredtointroduceanewproduct.The agencyclaims thatafterits campaign61%ofall consumersare familiarwith theproduct.Weask7randomlyselectedcustomers whetherornottheyarefamiliarwith theproduct. (a) findtheprobability that,outof7 customers,exactly4arefamiliarwith theproduct; (b) find the probability that at least 3 customers are familiar with the product; and (c) find the probability that at most 5 are familiar with the product.

**15. **Themeannumberofcarsperminutegoing throughthe Eisenhowerturnpikeautomatictoll is about7.Findtheprobability that exactly3will gothroughin agivenminute.

**16. **Labelthefollowing ascontinuousordiscretedistributions.

a) Thelengthsoffishin acertainlake.

b) Thenumberoffishinacertainlake.

c) Thediameterof15treesin aforest.

d) How manytreesareonafarmer'sacre.

**17. **Onadrysurface,thebrakingdistance(in meters)ofacertaincar is anormaldistribution with µ = 45.1mandσ = 0.5

**(a) **Findthebrakingdistancethatrepresentsthe91stpercentile.

**(b) **Findtheprobability thatthebrakingdistanceis less thanor equalto45m

**(c) **Findtheprobability thatthebrakingdistanceis greaterthan

46.8m

**(d) **Findtheprobability thatthebrakingdistanceis between45m and46.8m

**18. **Adrugmanufacturerwantstoestimatethemeanheartratefor patientswith acertainheartcondition.Themanufacturerfinds62peoplewith thecondition.Fromthis sample,themeanheartrateis101beats perminutewith astandarddeviationof8.

**(a) **Finda99%confidenceintervalforthetruemeanheartrateofall peoplewith this condition.

**(b) **Interpretthis confidenceintervalandwrite asentencethat explainsit.

**19. **Determinetheminimumrequiredsamplesize ifyouwanttobe

80%confidentthatthesamplemeaniswithin 2units ofthepopulation meangivensigma= 9.4.Assumethepopulationis normally distributed.

**20. **Asocialserviceworkerwantstoestimatethetrueproportionof pregnantteenagerswho miss atleastonedayofschool perweekon average.Thesocialworkerwantstobewithin 5%ofthetrue proportionwhenusing a90%confidenceinterval.Apreviousstudy estimatedthepopulationproportionat0.21.

**(a) **Using this previousstudyasanestimateforp,whatsamplesize should beused?

**(b) **Ifthepreviousstudywasnotavailable,whatestimateforp should beused?

**21. **Arestaurantclaims thatits speedofservicetimeis less than15 minutes.Arandomselection of49servicetimeswascollected,and theirmeanwascalculatedtobe14.5minutes.Theirstandard deviation is 2.7minutes.Isthereenoughevidencetosupportthe claim atalpha= .07.Performanappropriatehypothesistest,showing eachimportantstep.(Note:1stStep:WriteHo andHa; 2ndStep: DetermineRejection Region; etc.)

## [Solved] Final Exam Review Questions Solutions Guide

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- Submitted On 25 Jul, 2020 09:34:47

- Youngsimpo
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