Directions: Show all work. When using the calculator write down the function buttons used. not just write numerical solution write

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1 MAT 1272 Practic Exercises fr the Final Revised Spring 2017 (Ellner) Directins: Shw all wrk. When using the calculatr write dwn the functin buttns used. D nt just write a numerical slutin write A SENTENCE indicating what answer represents. The answers have slutins this frmat. 1. Use the fllwing 20 values: 222, 233, 254, 241, 251, 268, 276, 220, 238, 253, 249, 236, 247, 256, 261, 227, 257, 244, 239, 242 t perfrm the fllwing tasks: a) Cnstruct a frequency distributin table using 6 classes. b) Draw a histgram fr the frequency distributin in part (a). c) Draw a frequency plygn fr the frequency distributin in part (a). 2. The data set belw is a sample f the Mathematics test scres f 10 students: 56, 96, 78, 67, 60, 69, 85, 90, 89, 72 (a) Find the mean and median f the given test scres. (b) Is there a mde value fr these scres? Why r why nt? (c) Find the range and standard deviatin (nearest hundredth) f these scres. (d) Find the percentile rank f 78 (e) What percent f these scres are within 1 standard deviatin frm the mean? 3) a) Draw a Stem and Leaf Graph using the fllwing data: 22, 31,42, 49, 35, 24, 58, 61, 73, 24, 32, 42, 98, 61, 58 b) Prepare a bx and whisker plt fr these values indicate an utliers. 4. The chart belw recrds number f hurs 12 students spent nline during the weekend and the Math test scres they achieved the fllwing Mnday. Hurs n line (x) Test scres (y) I 96 I 75 I 84 I 82 I 74 I 76 I 85 I 95 I 68 I 50 I 65 I 58 I a) Draw the scatter plt b) Is there a psitive, negative r n relatinship between the number f hurs spent nline and the exam grade? c) Find the value f r, the linear regressin cnstant, and discuss whether this value cnfirms yur answer t part (b)? d) Find the equatin f the regressin line. e) Using the regressin line, predict, if pssible, the Math exam grade if a student was nline fr: i) 4 hurs ii) 5.5 hurs iii) 15 hurs. 5. The table belw shws the result f a survey in which 2000 students were asked hw they vted in the 2016 Presidential Electin. (Find prbabilities t fur decimal places.) Vted fr T Vted fr C Vted fr anther Did nt vte City Tech Males City Tech Females a) Find the prbability that a student in this grup did nt vte. b) Given that a student vted fr C, find the prbability the student was female? c) Find the prbability that a student was Male r Vted fr anther candidate. d) Are the categries did nt vte and vted fr C mutually exclusive? Why? e) What is the prbability that the student did nt vte fr T? 1

2 6. A bx cntains 15 red, 10 blue, and 5 green marbles. a) Tw marbles are selected at randm with replacement. Find the prbability they are bth red. b) Tw marbles are selected at randm withut replacement. Find the prbability that the first is blue and the secnd is green. c) Tw marbles are selected at randm withut replacement. Find the prbability that the first is blue and the secnd is yellw. 7. The table shws the result f a survey given t 250 randmly selected students wh were waiting fr Advisement in the Fall Ging fr an Ging fr a Neither Assciate s Degree Bachelr s Degree Receiving TAP Nt Receiving TAP a) Find the prbability that a student frm this grup is receiving TAP and is ging fr a Bachelr s Degree? b) Given that a student frm this grup is receiving TAP what is the prbability that the student is ging fr an Assciates Degree? c) What is the prbability that a student is ging fr an Assciates Degree? d) Are the categries ging fr an Assciate s Degree and receiving TAP independent? Why r why nt? 8. a) A club elects a president, vice president, secretary and treasurer. Hw many different sets f fficers are pssible if there are 10 members t chse frm? b) In a grup f 10 peple, 4 will each win $500. Hw many wining grups are pssible? Arrangement des nt matter. c) Hw many five digit zip cdes can be made, where the pssible digits are the numbers frm 0 thrugh 9, and n repeats are allwed? d) Hw many five digit zip cdes can be made, where the pssible digits are the numbers frm 0 thrugh 9, and repeats are allwed? 9. A study grup is t be selected frm a grup f 16 students. The grup cnsists f 5 freshmen, 7 sphmres, and 4 junirs. a) In hw many ways can a grup f 6 students be selected frm this grup? b) If the study grup is t cnsist f 2 freshmen, 3 sphmres, and 1 junir, hw many different grups are pssible? c) What is the prbability that a grup f 6 students will cnsist f 2 freshmen, 3 sphmres and 1 junir? 10. Let x be the number f PC cmputers are repaired at the Best Buy in Green Acres Mall n a randmly selected day. This data is represented in the discrete prbably distributin table belw (x) P(x) I? I 0.20 I 0.14 I a) Find the prbability that 3 cmputers were repaired that day. b) Find the mean f this prbability distributin c) Find the standard deviatin f this prbability distributin d) Find prbability that at mst 4 cmputers were repaired. 2

3 11. Accrding t the Natinal Institute f Health 32% f all wmen fracture a hip by the age f 90. If 8 wmen aged 90 are selected at randm, a) What is the prbability that exactly 5 suffered frm a hip fracture? b) What is the prbability that at mst 3 suffered frm a hip fracture? c) What is the prbability that nne suffered frm a hip fracture? d) What is the prbability that at least ne had a hip fracture? 12. In a recent race, the finish times frmed a nrmal distributin with a mean f 210 minutes and a standard deviatin f 25 minutes. a)find the z scre f Jse, wh finished in 190 minutes. b)find the z scre f Estella, wh finished in 270 minutes c) What is the prbability that a racer finished in less than 180 minutes? d)what is the prbability a racer finished between 190 and 225 minutes? 13. A prfessr determined that the grades n the Statistic Final are nrmally distributed with a mean grade f 68 and a standard deviatin f 15 a) If Mhammed had a z scre f 1.25, what was his grade? b) Students in the tp 12 % receive an A the student what is the lwest grade a student can get and still get an A? c) Students in the bttm 15% will fail the curse. What is the cutff grade a student can get and still pass? 14. The number f majr earthquakes in a year frms an apprximately nrmally distributed with a mean f 20.8 and a standard deviatin f 4.5. a) Find the prbability that in a given year there will be less than 21 earthquakes. b) Find the prbability that in a given year there will be between 18 and 23 earthquakes. 15. The tires manufactured by the ABC Tire Cmpany last an average f 42,000 miles with a standard deviatin f 7800 miles. If a randm sample f 100 the tires, manufactured by the ABC Tire Cmpany is taken, what is the prbability that these tires: a) will last mre than 41,000 miles? b) will last less than 43,250 miles? c) will last between 41,000 and 43,250 miles? 16. Fifty eight percent f all adults plan t purchase a Fitbit next year. Yu randmly select 200 adults and ask them if they plan t buy a Fitbit next year. What is the prbability that at least 120 f these adults will say they will buy a Fitbit next year? 17. A survey f all City Tech students fund that 35% say they get their lunch frm the salad bar in the cafeteria. A randm sample f 140 students is selected and asked if they get their lunch frm the salad bar in the cafeteria. a) What is the prbability that at mst 55 say they get their lunch frm the salad bar in the cafeteria? b) What is the prbability that mre than 40 say they get their lunch frm the salad bar in the cafeteria? c) What is the prbability that between 50 and 60, inclusive, say they get their lunch frm the salad bar in the cafeteria? 3

4 18. In the past, all patrns f a cinema cmplex have spent an average f $5.00 fr ppcrn and ther snacks, with a standard deviatin f $1.80. If a randm sample f 32 patrns is taken, what is the prbability that the mean expenditure f this sample is greater than $4.20? 19. Fr each f the fllwing claims i) State the Null Hypthesis H 0 and the Alternate Hypthesis H A ii) Indicate which is the claim. iii) Determine whether the reject regin is left tailed, right tailed r tw tailed. a) A cnsumer magazine reprts that the mean life f a dt matrix printer is at least 3.5 years. b) A realtr claims that rent fr studi apartments in new buildings in Brklyn cannt be $1500 a mnth. c) A car dealer annunces that the mean time fr an il change in its service department is less than 20 minutes. Fr questins answer all the fllwing questins: a)state the Null and Alternate Hyptheses b) Which is the claim? c) Describe the reject regin as left tailed, right tailed r tw tailed. d) Will yu use a z test r a t test? What is the critical value? e) Find the sample statistic. f) D yu reject r fail t reject the claim? Write ut yur decisin in at least ne sentence. 20. A reprt by a restaurant reviewer claims that serving staff, at all casual dining restaurants in New Jersey, receive at least $100 in tips with a standard deviatin f $15. Clleen, wh wrks as a server, in a casual dining restaurant in New Jersey, believes this claim is wrng. She recrds her tips ver a 30 day, perid and finds that they average $93. Using a 1% significance level test the claim. 21. It is claimed that the average annual per persn spending n all prescriptin drugs is $ 410 with a standard deviatin f $45. A survey f 64 randmly selected individuals fund that average annual per persn spending was $425. Using a 5% significance level test this claim. 22. A used car dealer says that the mean price f all 2009 Tyta Camry in Atlanta is at least $16,200. T test this claim yu search the Internet and get the prices f a randm sample f 14, f these cars available in Atlanta. The mean price f these cars is $15,999 with a standard deviatin f $1057. Is there enugh evidence t reject the dealer s claim at the 5% significance level? Assume the ppulatin is nrmal. 23. The help line at Wiley Publishers claims that the mean wait time t be cnnected is 6.8 minutes. Yu randmly select a sample f 19 callers and calculate their mean wait times t be 6.7 minutes with a standard deviatin f 1.24 minutes. Is there enugh evidence t reject the claim at a 5% significance level? Assume the ppulatin is nrmally distributed. 4

5 Fr questins answer all the fllwing questins: a)state the Null and Alternate Hyptheses b) Which is the claim? c) Will yu use a z test, t test r chi square test? What is the critical value? d) Describe the reject regin as left tailed, right tailed r tw tailed. e) Find the sample statistic. f) D yu reject the claim? Write ut yur decisin in at least ne sentence. 24. The Healthy Fd Cmpany makes an Oatmeal and Almnd cereal. It has three cmpetitrs wh make a similar prduct. The cmpany wants t investigate if the percentage f peple wh cnsume Oatmeal and Almnd cereal is the same fr each f the fur brands. Let A represent the Healthy Fd Cmpany s and B, C and D represent the 3 cmpetitrs. A sample f 1000 persn wh cnsume Oatmeal and Almnd cereal and they were asked which brand they cnsumed. The results are prvided in the table belw. Cereal Brand A B C D Cnsumptin Des the sample prvided n this table prvide enugh evidence t reject the null hypthesis that the percentage f peple wh cnsume Oatmeal and Almnd cereal is the same fr all fur brands? Use a significance level f 5% 25. The Smkey Bear Rangers statin came ut with a reprt in 2010 that said 61% f frest fires are started by accident, 24% by lighting, 13% by arsn and 2% f the causes are unknwn. A 2017 study f 1000 randmly selected frest fire fighting cmpanies was taken and the results f this sampling is recrded belw. Cause f Frest Fire Accident Lighting Arsn Unknwn Number recrded Assuming the Smkey Bear Rangers percentages are crrect fr the year 2010 test at the 2.5% significance level whether the current distributin f the causes f frest fires is different frm the 2010 reprt. MAT 1272 Answers t Practice Final Examples 1 (a) Class Frequencies

6 2. (a) The mean and median f these test scres are 76.2 respectfully 75. (b) There n mde because all the test scres unique. (c) The range is 40. The standard deviatin (t the nearest hundredth) is (d) A scre f 78 is in the 50 th percentile. (e) 60% f these test scres are within 1 standard deviatins f the mean. key strkes n calculatr STAT EDIT L1 ; STAT CALC (1) 1 Var 3. Stem Leaf [ Q1 Q2 Q3 IQR = Q3 Q1= 30 Since (30)= 109 and (30) = 14 there are n utliers 4. b) There is a negative relatinship between the number f hurs spent nline ver the weekend and the student s exam grade n the fllwing Mnday. c) The linear regressin cnstant r = Indicating a strng negative relatinship and cnfirms the answer t part (b) d) The equatin f the regressin line is y = 4.067x e) i) Predicted grade is 78. ii) Predicted grade is 72. iii) Cannt predict grade because15 hurs is utside the range f the data. key strkes n calculatr STAT EDIT L1 and L2. STAT CALC (4) LinReg. Be sure Diagnstic is n t get r value. 5. a) The prbability that a student in this grup did nt vte is a b) The prbability that a student wh vted fr C was female is c) The prbability that a student was Male r Vted fr anther candidate is d) The categries are mutually exclusive they have n members in cmmn. e) The prbability that a student did nt vte fr T is a) The is a.25 chance they are bth red. b) The prbability the first is blue and the secnd is green is c) There is a 0 prbability that the first is blue and the secnd is yellw 7. a) The prbability that a student s receiving TAP and ging fr a Bachelr s Degree is b) There is a prbability that a student wh is receiving TAP is ging fr an Assciates Degree. c) There is a prbability that a student is ging fr an Assciates Degree. 6

7 d) The categries ging fr an Assciate s Degree and receiving TAP are nt independent. P(Ass deg) P (Ass. / Tap). 8. a) There are 5040 different pssible sets f fficers. b) There are 210 pssible wining grups. key strkes n calculatr: MATH PRB (2) npr : : MATH PRB (3) ncr c) There are 30,240 zip cdes if n repeats are allwed. d) There are 100,000 zip cdes if repeats are allwed. 9. a) There are 8008 different ways a grup f 6 students can be selected. b) There are 1400 different ways the grup will cnsists f 2 freshman, 3 sphmres and ne junir. c) The prbability that the grup described abve will be frmed ut f these 16 individuals is 1400/8008 = key strkes n calculatr: MATH PRB (2) npr : : MATH PRB (3) ncr 10. a) The prbability f repairing 3 cmputers is 0.28 b) The mean is 2.94 cmputers. c) The standard deviatin is apprximately 1.3 cmputers key strkes n calculatr STAT CALC 1 Var Stat L1, L2 d) The prbability that at mst 4 cmputers were repaired is a)the prbability that exactly 5 had a hip fracture is Use Binmial Frmula sectin r key strkes n calculatr 2 nd VARS (10) binmial pdf (trials, p, x) b) The prbability that at mst 3 had a hip fracture is key strkes n calculatr 2 nd VARS (10) binmial cdf (trials, p, x) c) The prbability that nne fractured their hip is key strkes n calculatr 2 nd VARS (11) binmial pdf (trials,p,x) d) The prbability that at least ne had a hip fracture is a) The z scre f Jse is 0.8. b) The z scre fr Estella is 2.4 c) The prbability a racer finished in less than 180 minutes is d) The prbability a racer finished between 190 and 225 minutes is key strkes n calculatr 2 nd VARS (2) nrmal cdf (lwer, upper,, ) 13. a) Mhammed had a grade f b) The lwest grade t get an A is c) The lwest grade a student can get and still pass is key strkes n calculatr 2 nd VARS (3) invnrm(area,, ) 14. a) There is a prbability there will be less than 21 earthquakes in a given year. b) There is a prbability there will be between 18 and 23 earthquakes in a given year. 15. a) Using the calculatr there is a prbability a tire will last mre than 41,000 miles. Using the z scre table the z scre is 1.28 and there is a = prbability a tire will last mre than 41,000 miles. b) Using the calculatr there is a prbability a tire will last less than 43,250 miles. Using the z scre table the z scre is 1.60 and there is a prbability a tire will last mre than 43,250 miles. 7

8 c) Using z scres there is a prbability a tire will last between 41,000 and 43,250 miles. Using the calculatr this prbability is key strkes n calculatr 2 nd VARS nrmal cdf (lwer, upper,, ) 16. The prbability that at least 120 f these adults say they will buy a Fitbit next year varies slightly accrding the methd used. key strkes n calculatr 2 nd VARS (10) binmial cdf (trials, p, x)=p: 1 P = Or Binmial apprximatin t the Nrmal Distributin P(x > 119.5) = key strkes n calculatr 2 nd VARS (2) nrmal cdf (lwer, upper,, ) 17. Binmial Distributin 22 nd VARS (10) binmial cdf (140,.35, x) a) x = 55 P= is the prbability that at mst 55 get their lunch at the salad bar. b) x = 40 P =.0644 is prbability f 40 r less =.9356 is the prbability f mre than 40 get their lunch at the salad bar. c) binmial cdf (140,.35, 60) binmial cdf (140,.35, 50)=0.439 is the prbability that between 50 and 60, inclusive, get their lunch at the salad bar. 18. The prbability the mean expenditure f this sample is greater than $4.20 is key strkes n calculatr 2 nd VARS (2) nrmal cdf (lwer, upper,, ) 19. a) H 0 > 3.5 years CLAIM H A mean < 3.5 years left tailed b) H 0 rent mean = $1500 H A rent mean $1500 CLAIM tw tailed c) H 0 > 20 minutes H A mean < 20 minutes CLAIM left tailed 20. a) H tips > $100 H A tips < $100 b) The Null is the claim c) The reject regin is in the left tail d) Critical z, z0 = e) Sample statistic = 2.56 f) The sample statistic falls in the reject regin. Therefre the claim is rejected and waiters and waitresses at a casual dining restaurant d nt make an average f at least $100 per night in tips when tested at a 0.01 significance level. 21 a) H : = 410 H A : 410 b) H :l is the claim c) The tw tail reject regin area f ½ the significance level in each. d) Critical z, s are z0 = 1.96 e) Sample statistic = 2.67 f) The sample statistic falls in the reject regin. Therefre the claim is rejected. There is nt enugh evidence, at the 5% significance level, that the average annual per persn spending n prescriptin drugs is $ a) H mean > $16200 H A tips < $16200 b) H is the claim c) The reject regin is in the left tail d) Critical t, t0 = e) Sample statistic = f) The sample statistic des nt fall in the reject regin. Therefre we fail t reject H the used car dealer s claim is nt rejected at a 0.05 significance level. 23. a) H : = 6.8 minutes H A : 6.8 b) His the claim c) The tw tails make up the reject regin area f ½ the significance level in each. d) Critical t s are t0 = e) Sample statistic = f) The sample statistic des nt fall in the reject regin. We failed t reject H Therefre there is nt enugh evidence t reject the claim. There is enugh evidence, at the 5% significance level, that the mean waiting time t be cnnected is 6.8 minutes. 8

9 24. H : The percent f peple wh cnsume Oatmeal & Almnd cereal is the same fr all fur brands. H A : The percent f peple wh cnsume Oatmeal & Almnd cereal is nt the same fr all fur brands. : b) H is the claim c) Chi square test because 4 categries f qualitative data. 2 =7.815 d) Chi square is always right tailed. e) Sample statistic = f) Reject the claim that the percentage f cnsumptin f this cercal is the same fr all fur brands at the 5% significance level. 24 s it appears the recent percentages seem t be the same as thse fund in 2010 at the 5% significance level. 25. a) H : The current percentages are the same as thse recrded in H A : The current percentages are different frm thse recrded in b) H is the claim. c) Chi square test because 4 categries f qualitative data. 2 =9.348 d) Chi square is always right tailed. e) Sample statistic = f) Fail t reject the claim s it appears the recent percentages seem t be the same as thse fund in 2010 at the 2.5% significance level. 9