ࡱ> F -bjbjT~T~ 66e%5UU8C&*&&&4C6C6C6C6C6C6C$E}HFZC&z&"&&&ZCUU oCd+d+d+& U84Cd+&4Cd+d+>@ZsC(t? CC0C?\HV)H0@H@8&&d+&&&&&ZCZCd+&&&C&&&&H&&&&&&&&& : Chapter 5.1 # 7, 9, 11, 13, 15, 17, 19, 25, 27 For exercises 6 through 11, determine whether the distribution represents a probability distribution. If it does not, state why. X36812P(x)0.30.50.7-0.87. No, we cannot have negative numbers, and P(x) does not equal 1. X12345P(x) EMBED Equation.DSMT4  QUOTE   EMBED Equation.DSMT4  QUOTE   EMBED Equation.DSMT4  QUOTE   EMBED Equation.DSMT4  QUOTE   EMBED Equation.DSMT4  QUOTE  9. = EMBED Equation.DSMT4  = 1, yes 1. Each P(x) is between 0 and 1.  EMBED Equation.DSMT4 . X51015P(x) EMBED Equation.DSMT4 1.2 EMBED Equation.DSMT4 0.3 EMBED Equation.DSMT4 0.511.  EMBED Equation.DSMT4 , No, not equal to 1. 1. P(x) = 1.2 is not between 0 and 1, 2.  EMBED Equation.DSMT4  For Exercises 12 through 18, state whether the variable is discrete or continuous. 13. The number of cheeseburgers a fast-food restaurant serves each day. Discrete 15. The weight of a Siberian tiger. Continuous 17. The number of mathematics majors in your school. Discrete For Exercises 19 through 26, construct a probability distribution for the data and draw a graph for the distribution. 19. Medical tests the probabilities that a patient will have 0, 1, 2, or 3 medical tests performed on entering a hospital are  EMBED Equation.DSMT4  respectively. XP(X)06/1515/1523/1531/15 25. Student Classes The probabilities that a student is registered for 2, 3, 4, or 5 classes are 0.01, 0.34, 0.62, and 0.03, respectively.   27. Selecting a Monetary Bill A box contains three $1 bills, two $5 bills, five $10 bills, and one $20 bill. Construct a probability distribution for the data if x represents the value of a single bill drawn at random and then replaced.  Chapter 5.2 #3, 7, 11, 12, 13, 15, 18 3. Number of Credit Cards A bank vice president feels that each savings account customer has, on average, three credit cards. The following distribution represents the number of credit cards people won. Find the mean, variance, and standard deviation. Is the vice president correct? Number of Credit Cards X 0 1 2 3 4Probability P(X)0.180.440.270.080.03 Mean:  EMBED Equation.DSMT4  Variance  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Standard deviation  EMBED Equation.DSMT4  No, the vice president is not correct. On average, each person has about one credit card. 7. Commercials during childrens TV programs a concerned parents group determined the number of commercials shown in each of five childrens programs over a period of time. Find the mean, variance, and standard deviation shown. Number of commercials X56789Probability P(x)0.20.250.380.100.07  EMBED Equation.DSMT4  EMBED Equation.DSMT4 P(x)X EMBED Equation.DSMT4 P(x) EMBED Equation.DSMT4  EMBED Equation.DSMT4 P (x)5250.2156360.251.597490.382.6618.628720.100.86.49810.070.635.67Sum =6.5944.69 EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4  11. Insurance an insurance company insures a persons antique coin collection worth $20,000 for an annual premium of $300. If the company figures that the probability of the collection being stolen is 0.002, what will be the companys expected profit? P (of being stolen) = 0.002 Worth=20,000 P (of not being stolen) = 0.998 premium=300=20,000-300=19,700 xP(x)x EMBED Equation.DSMT4 p(x)Profit3000.998299.4Loss-19,7000.002-39.4Sum = 260 Expected profit is $260.0. 12. Job Bids a landscape contractor bids on jobs where he can make $3000 profit. The probabilities of getting one, two, three, or four jobs per month are shown. Number of jobs X1234Probability P(x)0.20.30.40.1 Find the contractors expected profit per month. Mean:  EMBED Equation.DSMT4  Per month the contractors expected profit is 2.4($3000) = $7200 13. Rolling Dice if a person rolls doubles when he tosses two dice, he wins $5. For the game to be fair, how much should the person pay to play the game? WinGain x$5 Probability P(x)1/6  EMBED Equation.DSMT4  Therefore, he has to pay $0.83 for the game to be fair. 15. Lottery prizes a lottery offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. Find the expectation if a person buys one ticket. xP(x)x EMBED Equation.DSMT4 p(x)win1000-31/1000997/1000win500-31/1000497/1000win100-35/1000485/1000loss-3993/1000-2979/1000Sum =-1000/1000=-1 EMBED Equation.DSMT4  Expectation of buying one ticket is losing one dollar Or -$1.00. 18. Life Insurance a 35-year-old woman purchases a $100,000 term life insurance policy for an annual payment of $360. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999057. Find the expected value of the policy for the insurance company. WinLoseGain X$360-99,640Probability P(X)0.9990570.000943  EMBED Equation.DSMT4  The expected value of the policy for the insurance company is $265.70 Section 5-3 #s 1, 3ae, 5, 7, 11, 14bgh, 15, 17 ,19, 21 ,25 1) Which of the following are binomial experiments or can be reduced to binomial experiments? Surveying 100 people to determine if they like Sudsy Soap Yes Tossing a coin 100 times to see how many heads occur Yes Drawing a card with replacement from a deck and getting a heart Yes Asking 1000 people which brand of cigarettes they smoke No Testing four different brands of aspirin to see which brands are effective No Testing one brand of aspirin by using 10 people to determine whether it is effective Yes Asking 100 people if they smoke Yes Checking 1000 applicants to see whether they were admitted to White Oak College Yes Surveying 300 prisoners to see how many different crimes they were convicted of No Surveying 300 prisoners to see whether this is their first offense Yes 3) Compute the probability of X successes, using the binomial formula.  EMBED Equation.DSMT4  n=6, X=3, p=0.03 then q= 1 -0.03 = 0.97  EMBED Equation.DSMT4  EMBED Equation.DSMT4  n=10, X=5, p=0.37 then q= 1 0.37 = 0.63  EMBED Equation.DSMT4  5) True/False Exam a student takes a 20-question, true/false exam and guesses on each question. Find the probability of passing if the lowest passing grade is 15 correct out of 20. Would you consider this event likely to occur? Explain your answer. n=20, X EMBED Equation.DSMT4 15, p= EMBED Equation.DSMT4 , q= EMBED Equation.DSMT4   EMBED Equation.DSMT4  No, this event would not likely occur because its only about a 2% chance. 7) Driving to Work Alone It is reported that 77% of workers aged 16 and over drive to work alone. Choose 8 workers at random. Find the probability that a. All drive to work alone  EMBED Equation.DSMT4  b. More than one-half drive to work alone  EMBED Equation.DSMT4  c. Exactly 3 drive to work alone  EMBED Equation.DSMT4  11) College Education and Business World Success R. H. Bruskin Associates Market Research found that 40% of Americans do not think that having a college education is important to succeed in the business world. If a random sample of five Americans is selected, find these probabilities. a) Exactly two people will agree with that statement. n=5, p=0.4, q=0.6, X=2  EMBED Equation.DSMT4  b) At most three people will agree with that statement. n=5, p=0.4, q=0.6, X=2  EMBED Equation.DSMT4  c) At least two people will agree with that statement.  EMBED Equation.DSMT4  d) Fewer than three people will agree with that statement.  EMBED Equation.DSMT4  14) Find the mean, variance, and standard deviation for each of the values of n and p when the conditions for the binomial distribution are met.  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  15) Social Security Recipients A study found that 1% of social security recipients are too young to vote. If 800 social security recipients are randomly selected, find the mean, variance, and standard deviation of the number of recipients who are too young to vote.  EMBED Equation.DSMT4  17) Defective Calculators If 3% of calculators are defective, find the mean, variance, and standard deviation of a lot of 300 calculators.  EMBED Equation.DSMT4  19) Watching Fireworks a survey found that 21% of Americans watch fireworks on television on July 4. Find the mean, variance, and standard deviation of the number of individuals who watch fireworks on television on July 4 if a random sample of 1000 Americans is selected.  EMBED Equation.DSMT4  21) Survey on Bathing Pets a survey found that 25% of pet owners had their pets bathed professionally rather than do it themselves. If 18 pet owners are randomly selected, find the probability that exactly five people have their pets bathed professionally. n=18, p=0.25, q=0.75, X=5  EMBED Equation.DSMT4  25) Survey on Internet Awareness In a survey, 58% of American adults said they had never heard of the Internet. If 20 American adults are selected at random, find the probability that exactly 12 will say they have never heard of the Internet.  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11000)++100g( 51000)"-3=="-1.00 FMathType 6.0 Equation MathType EFEquation.DSMT49q<LPR<DSMT6WinAllBasicCodePages_1293553890F@-sC@-sCOle CompObjiObjInfoEquation Native _1293467491:F@-sC@-sCOle CompObjiTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  E(x)==m=="xgp(x)==360(.999057)"-99640(.000943)==265.70 FMathType 6.0 Equation MathType EFEquation.DSMT49qEPR<DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(X)== n!(n"-X)!X!gObjInfoEquation Native _1293467740F@-sC@-sCOle p X gq n"-X == n C X gp X gq n"-X FMathType 6.0 Equation MathType EFEquation.DSMT49qEPR<DSMT6WinAllBasicCodePagesCompObjiObjInfoEquation Native _1293467442F@-sC@-sCTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(X)== 6 C 3 g0.03 3 g0.97 6"-3 ==20(0.000027)(0.912673)==0.0005Ole CompObjiObjInfoEquation Native   "#$'*+,/23456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\_bcdefghknopqrstuvwxyz{|}~ FMathType 6.0 Equation MathType EFEquation.DSMT49qEPR<DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   _1293467778F@-sC@-sCOle CompObj iObjInfo  FMathType 6.0 Equation MathType EFEquation.DSMT49qEPR<DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(X)== Equation Native  $_1293468655F@-sC@-sCOle CompObji10 C 5 g0.37 5 g0.63 10"-5 ==252(0.37) 5 (0.63) 5 ==0.173 FMathType 6.0 Equation MathType EFEquation.DSMT49qObjInfoEquation Native _1293468709F@-sC@-sCOle ETPRDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  e" FMathType 6.0 Equation MathType EFEquation.DSMT49qCompObjiObjInfo Equation Native !_1293468728F@-sC@-sCE,PRTDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   12 FMathType 6.0 Equation MathType EFEquation.DSMT49qOle %CompObj&iObjInfo(Equation Native )E<PRTDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   12 FMathType 6.0 Equation MathType EFEquation.DSMT49q_1293468673F@-sC@-sCOle -CompObj.iObjInfo0E PRDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(X)== 20 C 15 ( 12) 15 ( 12) 20"-15 ==15Equation Native 1 _1344184357F@-sC@-sCOle ]CompObj^i,504( 12) 15 ( 12) 5 ==0.015P(X)== 20 C 16 ( 12) 16 ( 12) 20"-16 ==4,845( 12) 16 ( 12) 4 ==0.005P(X)== 20 C 17 ( 12) 17 ( 12) 20"-17 ==1,140( 12) 17 ( 12) 3 ==0.001P(X)== 20 C 18 ( 12) 18 ( 12) 20"-18 ==190( 12) 18 ( 12) 2 ==0.0002P(X)== 20 C 19 ( 12) 19 ( 12) 20"-19 ==20( 12) 19 ( 12) 1 ==0.00002P(X)== 20 C 20 ( 12) 20 ( 12) 20"-20 ==1( 12) 20 ( 12) 0 ==0.000000954so...P(X)==0.015++0.005++0.001++0.0002++0.00002++0.000000954==0.021 FMathType 5.0 Equation MathType EFEquation.DSMT49qObjInfo`Equation Native a_1344184108]F@-sC0/sCOle i\DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  n==8,p==0.77,X==8P(X)== 8 C 8 (0.77) 8 (0.23) 0 ==0.124 FMathType 5.0 Equation MathType EFEquation.DSMT49q…\DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_ECompObjjiObjInfolEquation Native m_1344184160F0/sC0/sC_A  n==8,p==0.77,X==5,6,7,or8P(X)== 8 C 5 (0.77) 5 (0.23) 3 ++ 8 C 6 (0.77) 6 (0.23) 2 ++ 8 C 7 (0.77) 7 (0.23) 1 ++ 8 C 8 (0.77) 8 (0.23) 0 ==0.184 ++ 0.309 ++0.295 ++0.124==0.912Ole CompObjiObjInfoEquation Native  FMathType 5.0 Equation MathType EFEquation.DSMT49q\DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  n==8,p==0.77,X==3P(X)== 8 C 3 (0.77) 3 (0.23) 5 ==0.017 FMathType 6.0 Equation MathType EFEquation.DSMT49q_1295432485F0/sC0/sCOle CompObjiObjInfodPR|DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(X==2)== 5 C 2 (0.4) 2 (0.6) 3 ==0.346Equation Native _1295432516vF0/sC0/sCOle CompObji FMathType 6.0 Equation MathType EFEquation.DSMT49q\PR|DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(Xd"3)ObjInfoEquation Native _1295432753F0/sC0/sCOle ==P(x==0)++P(x==1)++P(x==2)++P(x==3)== 5 C 0 (0.4) 0 (0.6) 5 ++ 5 C 1 (0.4) 1 (0.6) 4 ++ 5 C 2 (0.4) 2 (0.6) 3 ++ 5 C 3 (0.4) 3 (0.6) 2 ==0.913 FMathType 6.0 Equation MathType EFEquation.DSMT49qCompObjiObjInfoEquation Native _1295432888F0/sC0/sC\PR|DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(xe"2)==1"-P(x<<2)==1"-(P(x==0)++P(x==1))==1"-(0.078++0.259)==0.663Ole CompObjiObjInfoEquation Native  FMathType 6.0 Equation MathType EFEquation.DSMT49q\PR|DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(x<<3)==P(x==0)++P(x==1)++P(x==2)==0.078++0.259++0.346==0.683 FMathType 6.0 Equation MathType EFEquation.DSMT49q_1293470858 F0/sC0/sCOle CompObjiObjInfoEquation Native ,_1293470673F0/sC0/sCOle CompObjiEPRDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  n==300,p==0.3m==300(0.3)==90s 2 ==300(0.3)(0.7)==63s== 63  ==7.94==7.9 FMathType 6.0 Equation MathType EFEquation.DSMT49qE,PRDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_EObjInfoEquation Native H_1293470572F0/sC0/sCOle _A  n==50, p== 25m==50( 25)==20s 2 ==50( 25)( 35)==12s== 12  ==3.464==3.5CompObjiObjInfoEquation Native /_1295433296F0/sC0/sC FMathType 6.0 Equation MathType EFEquation.DSMT49qEPRDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  n==36,p== 16m==36( 16)==6s 2 ==36( 16)( 56)==5s== 5  ==2.236==2.2 FMathType 6.0 Equation MathType EFEquation.DSMT49qOle CompObjiObjInfoEquation Native O3tPR|DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  m==n"p==800(0.01)==8s 2 ==n"p"q==800(0.01)(0.99)==7.9s== n"p"q  == 7.9  ==2.8 FMathType 6.0 Equation MathType EFEquation.DSMT49qEPRDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/AP_1293470980F0/sC0/sCOle CompObjiObjInfoEquation Native :_1295433623F0/sC0/sCOle CompObji   "%&'()*,-./01345678:;<>?@ABDG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  n==300,p==0.03m==300(0.03)==9s 2 ==300(0.03)(0.97)==8.73s== 8.73  ==2.95 FMathType 6.0 Equation MathType EFEquation.DSMT49q`PR<DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  m==n"p==1000(0.21)==2ObjInfo Equation Native  |_1293471260F0/sC0/sCOle 10s 2 ==n"p"q==1000(0.21)(0.79)==165.9s== n"p"q  == 165.9  ==12.9 FMathType 6.0 Equation MathType EFEquation.DSMT49qCompObjiObjInfoEquation Native _1293471246F0/sC0/sCEPRDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P(X)== 18 C 5 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