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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 Equations/316172: I need help solving this equation: a=3w+2p. I need to solve for w.1 solutions Answer 226140 by stanbon(57307)   on 2010-06-21 08:29:50 (Show Source): You can put this solution on YOUR website!I need help solving this equation: a=3w+2p. I need to solve for w. Subtract 2p from both sides: 3w = a-2p Divide both sides by 3: w = (a-2p)/3 ================= Cheers, Stan H. =================
 Polynomials-and-rational-expressions/316171: form a polynomial with real coefficients. -3-2i; 2 multiplicity 21 solutions Answer 226139 by stanbon(57307)   on 2010-06-21 08:28:16 (Show Source): You can put this solution on YOUR website!form a polynomial with real coefficients. -3-2i; 2 multiplicity 2 ---- Roots: -3-2i, -3+2i ; 2 with mult 2 --- f(x)= (x-(-3-2i))(x-(-3+2i))(x-2)^2 --- f(x) = ((x+3)+2i)((x+3)-2i)(x^2-4x+4) --- f(x) = ((x+3)^2 + 4)(x^2-4x+4) --- f(x) = (x^2+6x+9)(x^2-4x+4) =============================== Cheers, Stan H.
 Probability-and-statistics/316103: Suppose there were “x” students in a class who scored 100 and “y” students who scored 50. Write an algebraic expression for the mean in terms of “x” and “y”.1 solutions Answer 226138 by stanbon(57307)   on 2010-06-21 08:18:13 (Show Source): You can put this solution on YOUR website!Suppose there were “x” students in a class who scored 100 and “y” students who scored 50. Write an algebraic expression for the mean in terms of “x” and “y”. ---------------- average = (# of points)/(# of students) -------------------------------------------- Points: 100x Points: 50y # of students: x+y ----- Mean = Average = (100x+50y)/(x+y) =================================== Cheers, Stan H.
 Probability-and-statistics/316140: What is the critical value of that corresponds to a degree of confidence of 91%?1 solutions Answer 226137 by stanbon(57307)   on 2010-06-21 08:11:00 (Show Source): You can put this solution on YOUR website!What is the critical value of that corresponds to a degree of confidence of 91%? That depends on the type of test you are running: Left tail: invNorm(0.09) = -1.3408 Right tail: invNorm(0.91) = 1.3408 Two-tail: +-invNorm(0.045) = +-1.6954 ========================================== Cheers, Stan H.
 Probability-and-statistics/316141: A laboratory tested 70 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with s = 12 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content, μ, of all such eggs. 1 solutions Answer 226136 by stanbon(57307)   on 2010-06-21 07:58:31 (Show Source): You can put this solution on YOUR website!A laboratory tested 70 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with s = 12 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content, μ, of all such eggs. --------------------------- sample mean = 228 --- Max Error = E = (invT(0.975 with df = 69) = 1.9949*1.4343 = 2.86 --------------------- 95% CI: 228-2.86 < u < 228+2.86 =================================== Cheers, Stan H.
 Probability-and-statistics/316002: Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers). a. If you have a body temperature of 99.00 °F, what is your percentile score? b. Convert 99.00 °F to a standard score (or a z-score). c. Is a body temperature of 99.00 °F unusual? Why or why not? d. Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98 °F or lower? e. A person’s body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude? 1 solutions Answer 226093 by stanbon(57307)   on 2010-06-20 21:34:18 (Show Source): You can put this solution on YOUR website!Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers). a. If you have a body temperature of 99.00 °F, what is your percentile score? z(99) = (99-98.2)/0.62 = 1.2903 P(z < 1.2903) = normalcdf(-100,1.2903) = 0.9015 --- 99 degrees is at the 91%ile --------------------------------------------------------------- b. Convert 99.00 °F to a standard score (or a z-score). See the problem above. --------------------------------------- c. Is a body temperature of 99.00 °F unusual? Why or why not? Not too unusual. It is 1.29 standard deviations above the mean. --------------------------------------- d. Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98 °F or lower? z(97.98-98.2)/[0.62/sqrt(50)] = -2.5091 P(z< -2.5091) = 0.0061 --------------------------------------- e. A person’s body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude? ------------- Find the z-value of 101 degrees. Based on the z-value decide if the result is "unusual". ================================== Cheers, Stan H.
 Probability-and-statistics/316016: In a study of elephants a researcher wishes to determine the average weight of a certain subspecies of elephants. From previous studies, the standard deviation of the weights of elephants in this subspecies is known to be 1500 pounds. How many elephants does the researcher need to weigh so that he can be 80% confident that the average weight of elephants in his sample is within 350 pounds of the true average weight for this subspecies? A. 31 B. 39 C. 50 D. 166 1 solutions Answer 226092 by stanbon(57307)   on 2010-06-20 21:15:51 (Show Source): You can put this solution on YOUR website!From previous studies, the standard deviation of the weights of elephants in this subspecies is known to be 1500 pounds. -------------------------------------------------- How many elephants does the researcher need to weigh so that he can be 80% confident that the average weight of elephants in his sample is within 350 pounds of the true average weight for this subspecies? --------------- n = [z*s/E]^2 --- n = [1.2816*1500/350]^2 = 5.4924^2 = 30.16 n = 31 when rounded up ======================= Cheers, Stan H. ======================= A. 31 B. 39 C. 50 D. 166
 Probability-and-statistics/316030: find the z score that has 28.1% of the distribution's area to the left1 solutions Answer 226091 by stanbon(57307)   on 2010-06-20 21:08:29 (Show Source): You can put this solution on YOUR website!find the z score that has 28.1% of the distribution's area to the left ---------------------------- invNorm(0.281) = -0.5799 ============================= Cheers, Stan H.
 Probability-and-statistics/316063: Suppose that the time required to complete a 1040R tax form is normally distributed with a mean of minutes and a standard deviation of minutes. What proportion of 1040R tax forms will be completed in less than minutes? Round your answer to at least four decimal places. 1 solutions Answer 226090 by stanbon(57307)   on 2010-06-20 21:04:52 (Show Source): You can put this solution on YOUR website!Suppose that the time required to complete a 1040R tax form is normally distributed with a mean of ? minutes and a standard deviation of ?? minutes. What proportion of 1040R tax forms will be completed in less than minutes? Round your answer to at least four decimal places. --------------------------------------------------- Numbers are missing in your post. See ? and ??. ------------------------------- Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/316061: Ronald wants to sell his car through a broker who charges a commission of 10% of the selling price. Ronald still owes \$11,025 on the car. Ronald must get enough to at least pay off the loan. What is the range of the selling price? x-0.10x=11025 0.90x=11025 x=11025/.90 11025.9 Amount range needed; 12,127.61 solutions Answer 226087 by stanbon(57307)   on 2010-06-20 20:52:28 (Show Source): You can put this solution on YOUR website!Ronald wants to sell his car through a broker who charges a commission of 10% of the selling price. Ronald still owes \$11,025 on the car. Ronald must get enough to at least pay off the loan. What is the range of the selling price? x-0.10x=11025 0.90x=11025 x=11025/.90 x = \$12250 --- Range: >= \$12250 -------------------- Cheers, stan H. ====================
 Probability-and-statistics/316012: a microwave oven repairer says that the mean repair cost for damaged microwave ovens is less than \$90. You work for the repairer and want to test this claim. You find that a random sample of five microwave ovens has a mean repair cost of \$68 and a standard deviation of \$12. at alpha =0.10, do you have enough evidence to support the repairer's claim. assume the population is normally distributed1 solutions Answer 226063 by stanbon(57307)   on 2010-06-20 19:08:34 (Show Source): You can put this solution on YOUR website!a microwave oven repairer says that the mean repair cost for damaged microwave ovens is less than \$90. You work for the repairer and want to test this claim. You find that a random sample of five microwave ovens has a mean repair cost of \$68 and a standard deviation of \$12. at alpha =0.10, do you have enough evidence to support the repairer's claim. assume the population is normally distributed --------------------------- Ho: u >= 90 Ha: u < 90 (repairer's claim) ---------------- t(68) = (68-90)/[12/sqrt(5)] = -0.8188 --- p-value = P(t< -0.8188 when df = 4) = 0.2292 --- Since the p-value is greater than 10%, fail to reject Ho. The test results do not support the repairer' s claim. ================== Cheers, stan H.
 Probability-and-statistics/316013: The median can be a more appropriate measure of central tendency than the mean if the distribution of the data is extremely skewed. A. False B. True C. It doesn’t matter, when data are skewed the mean and the median are the same D. It doesn’t matter, when data are skewed the mean, median, and mode are the same 1 solutions Answer 226060 by stanbon(57307)   on 2010-06-20 18:52:33 (Show Source): You can put this solution on YOUR website!The median can be a more appropriate measure of central tendency than the mean if the distribution of the data is extremely skewed. ---------------- True If there is a lorge skew number it pulls the mean away from the center of the distribution. ======================= Cheers, Stan H. ======================= A. False B. True C. It doesn’t matter, when data are skewed the mean and the median are the same D. It doesn’t matter, when data are skewed the mean, median, and mode are the same
 Probability-and-statistics/316006: Bob was ranked 50th in a class of 250. What was his percentile rank?1 solutions Answer 226058 by stanbon(57307)   on 2010-06-20 18:46:05 (Show Source): You can put this solution on YOUR website! Bob was ranked 50th in a class of 250. What was his percentile rank? ----- # of scores below Bob's score = 49 ---- % of scores below his score = (49/250) = 19.6% --- Bob's score is 19%ile ========================== Cheers, Stan H.
 real-numbers/315895: how can you show that each number is a rational number? 1 solutions Answer 225991 by stanbon(57307)   on 2010-06-20 09:35:56 (Show Source): You can put this solution on YOUR website!Each number is NOT a rational number. Rational numbers can be written in the form a/b where a and b are integers and b is not zero. -------------------- Lots of numbers cannot be written in that form. A bunch of them are called irrational numbers. Examples are: sqrt(2), sqrt(3), pi, e, sqrt(any number that is not a perfect square) ..... ------------------ Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/315900: find the first second and third number of 1/3x+1/7(x+1)=1/2(x+2)-2 find the smallest and larger number of 1/3(x+2)-1/5x=12 find the first second and third number of x+1/2(x2)+1/4(x+4)=2x-281 solutions Answer 225990 by stanbon(57307)   on 2010-06-20 09:31:58 (Show Source): You can put this solution on YOUR website!find the first second and third number of 1/3x+1/7(x+1)=1/2(x+2)-2 --- Multiply thru by 42 to get: 14x + 6(x+1) = 21(x+2)-84 --- 20x + 6 = 21x-42 x = 48 -- x+1 = 49 --- x+2 = 50 ================= Cheers, Stan H. ==================
 Probability-and-statistics/315893: A statistician working for the Department of Interior is constructing a systematic random sample of trees in a forest preserve. All threes have been identified and numbered with a non-invasive number attached to each bark. The statistician wishes to estimate the mean height of the trees in the forest preserve, and has calculated an appropriate sample size of n=43 trees. The 587th tree of 731 trees in the preserve was selected as the first observation in the sample. What is the number of the second observation in the sample?1 solutions Answer 225989 by stanbon(57307)   on 2010-06-20 09:28:17 (Show Source): You can put this solution on YOUR website!The statistician wishes to estimate the mean height of the trees in the forest preserve, and has calculated an appropriate sample size of n=43 trees. The 587th tree of 731 trees in the preserve was selected as the first observation in the sample. What is the number of the second observation in the sample? ------ If (and that is a big if) you think he will count another 587 trees, and will count tree number 1 as following tree 731, the answer would be: 587*2 = 1174 1174-731 = 443 His 2nd choice would be tree # 443 -------------------------------------- Mathematically this is a solution to 587 = x(mod 731) x = 587, 443, 299, etc ============================ Cheers, Stan H. ============================
 Quadratic_Equations/315898: 3+√(z-5)=√(z+10) please help me solve this equation thanks1 solutions Answer 225988 by stanbon(57307)   on 2010-06-20 09:18:34 (Show Source): You can put this solution on YOUR website!3+√(z-5)=√(z+10) --- Square both sides to get: 9 + 6sqrt(z-5) + (z-5) = z+10 --- Rearrange: 6sqrt(z-5) = 6 ---- sqrt(z-5) = 1 Square both sides: z-5 = 1 z = 6 ----- Check the "answer": 3 + sqrt(6-5) = sqrt(6+10) 3 + 1 = 4 4 = 4 --------------- Therefore: z = 6 ======================= Cheers, Stan H.
 Probability-and-statistics/315863: A bag contains 4 red and 2 green jelly beans, the second bag contains 2 red and 3 green jelly beans. A bag is selected at random and a jelly bean is randomly taken from it. The jelly bean is red. What is the probability that it came from the first bag? (Bayes's theorem)1 solutions Answer 225987 by stanbon(57307)   on 2010-06-20 09:14:34 (Show Source): You can put this solution on YOUR website!A bag contains 4 red and 2 green jelly beans, the second bag contains 2 red and 3 green jelly beans. A bag is selected at random and a jelly bean is randomly taken from it. The jelly bean is red. What is the probability that it came from the first bag? --------------- P(1st|red) = P(1st and red)/P(red) = [P(red|1st)*P(1st)]/[P(red and 1st + P(red and 2nd)] = [(4/6)*(1/2)]/[(4/6)*(1/2) + (2/5)(1/2)] = [(1/3)/[(1/3)+(1/5)] = (1/3)/(8/15) = 5/8 ============== Cheers, Stan H.
 Probability-and-statistics/315897: There are 315 student 112 are males the rest females, What is the probability that a person selected at random from the schools data will be male? 1 solutions Answer 225985 by stanbon(57307)   on 2010-06-20 08:55:28 (Show Source): You can put this solution on YOUR website!There are 315 student 112 are males the rest females, What is the probability that a person selected at random from the schools data will be male? --- P(pick a male) = 112/315 ============================== Cheers, Stan H.
 test/315835: Let f(x)=2x^2+8x+5. Suppose the graph of y=f(x) is shifted 2 units to the left and 1 unit up. Write an equation for the new graph.1 solutions Answer 225957 by stanbon(57307)   on 2010-06-19 23:33:14 (Show Source): You can put this solution on YOUR website!Let f(x)=2x^2+8x+5. Suppose the graph of y=f(x) is shifted 2 units to the left and 1 unit up. Write an equation for the new graph. g(x) = 2(x+2)^2 + 8(x+2) + 6 ============================== Cheers, Stan H.
 Probability-and-statistics/315840: A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, , of cars rented in the U.S. this year. The consumer group has reason to believe that the mean monthly mileage of cars rented in the U.S. this year is less than last year's mean, which was miles. The group plans to do a statistical test regarding the value of . It chooses a random sample of monthly mileages and computes the mean of the sample to be miles and the standard deviation to be miles. 1 What is the null hypothesis and the alternate hypothesis that should be used for the test? 2. In the context of this test, what is the Type II error? ( A type two error _______ the hypothesis that U is _________ ________ when in fact u is _______ ________) 3. Suppose the group decides not to reject the hypothesis. What sort of error might it be making ____? Now I beleive I got the first part: HO: u is less than 2850 H1: u is not equal to 2850 I just having a hard time understanding the other part 1 solutions Answer 225956 by stanbon(57307)   on 2010-06-19 23:31:13 (Show Source): You can put this solution on YOUR website!A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, of cars rented in the U.S. this year. The consumer group has reason to believe that the mean monthly mileage of cars rented in the U.S. this year is less than last year's mean, which was 2850 miles. The group plans to do a statistical test regarding the value of . It chooses a random sample of monthly mileages and computes the mean of the sample to be miles and the standard deviation to be miles. 1 What is the null hypothesis and the alternate hypothesis that should be used for the test? Ho: u >= 2850 miles Ha: u < 2850 miles ------------------------- Comment: Equality must ALWAYS be included in Ho. ------------------------- 2. In the context of this test, what is the Type II error? (A type two error is failing to reject the null hypothesis that u is greater than or equal to 2850 when in fact u is not greater than or equal to 2850) 3. Suppose the group decides not to reject the hypothesis. What sort of error might it be making. A type II error. Note: A type I error is the probability you reject Ho when in fact Ho is true A type II error is the probabioliity you fail to reject Ho when in fact Ho is false. =================== Cheers, Stan H. ===================
 logarithm/315739: Express as a sum, difference, and product of logarithms, without using exponents. logb sqrt a^7b^6/a^3b^4 1 solutions Answer 225907 by stanbon(57307)   on 2010-06-19 15:26:03 (Show Source): You can put this solution on YOUR website!Express as a sum, difference, and product of logarithms, without using exponents. logb sqrt a^7b^6/a^3b^4 ----- = logb[sqrt a^4*b^2] ---------- = logb[a^2b] = logb(a^2) + logb(b) = 2logb(a) + 1 ================= Cheers, Stan H.
 Linear-equations/315762: What is the slope of the line: 2y + 8x = 261 solutions Answer 225906 by stanbon(57307)   on 2010-06-19 15:17:23 (Show Source): You can put this solution on YOUR website! What is the slope of the line: 2y + 8x = 26 ----- 2y + 8x = 26 y + 4x = 13 y = -4x+13 ------- Slope is always the amount that y changes when x changes 1. --- slope = -4 ================ Cheers, Stan H.
 test/315756: What are the propertys for 3c+5(2+c)=3c+5(2)+5c =3c+5c+5(2) =(3c+5c)+5(2) =(3+5)c+5(2) =8c+10??1 solutions Answer 225905 by stanbon(57307)   on 2010-06-19 15:14:35 (Show Source): You can put this solution on YOUR website!answered Cheers, Stan H.
 Human-and-algebraic-language/315743: girls test scores in 1998 averaged 159, boys were 140, by 2002 girls were 160, boys were 136 so in 4 years the girls went up 1 pt. and the boys went down 4.Here is the formula given Girls W= 1/4x + 159. Boys W= -x + 140.W is the average writing score X years after 1998. 1.If current trends continue, when will the average test score for girls be 49 points higher than for boys? 2.If the current trends continue, when will the average test score for girls be 54 points higher than for boys? They printed the answer for #1 as the year 2022, but I don't know how to get it. If I could answer the 1st then the second should be easy. I don't know how to set it up.1 solutions Answer 225904 by stanbon(57307)   on 2010-06-19 15:13:09 (Show Source): You can put this solution on YOUR website! 4.Here is the formula given Girls W= 1/4x + 159. Boys W= -x + 140.W is the average writing score X years after 1998. 1.If current trends continue, when will the average test score for girls be 49 points higher than for boys? 2.If the current trends continue, when will the average test score for girls be 54 points higher than for boys? They printed the answer for #1 as the year 2022 Girls W= (1/4)x + 159. Boys W= -x + 140.W is the average writing score X years after 1998. 1.If current trends continue, when will the average test score for girls be 49 points higher than for boys? --- Equation: Girls = Boys + 49 (1/4)x+159 = -x+140 + 49 (5/4)x = 30 (1/4)x = 6 x = 24 --- Year: 1998+24 = 2022 =========================== Cheers, Stan H. ===========================
 Expressions-with-variables/315761: how can i do this problem 4m-2(3m+2)-4(m-1) 1 solutions Answer 225903 by stanbon(57307)   on 2010-06-19 14:56:04 (Show Source): You can put this solution on YOUR website!4m-2(3m+2)-4(m-1) ------ 4m-6m-4-4m+4 --- 4m-6m-4m-4+4 ---- -6m ======== Cheers, Stan H.
 test/315757: What propertys are 3c+5(2+c)=3c+5(2)+5c =3c+5c+5(2) =(3c+5c)+5(2) =(3+5)c+5(2) =8c+10??1 solutions Answer 225902 by stanbon(57307)   on 2010-06-19 14:52:13 (Show Source): You can put this solution on YOUR website!What propertys are 3c+5(2+c)=3c+5(2)+5c:::distributive ---- =3c+5c+5(2):::commutative -------- =(3c+5c)+5(2):::associative -------- =(3+5)c+5(2)::::distributive -------- =8c+10::::identity ============================== Cheers, Stan H.
 Probability-and-statistics/315568: The 3rd quartile on a set of data of sampled wind speeds in an area considering using wind power is 27.3 m/sec. Interpret its meaning. show work.1 solutions Answer 225895 by stanbon(57307)   on 2010-06-19 13:19:46 (Show Source): You can put this solution on YOUR website!The 3rd quartile on a set of data of sampled wind speeds in an area considering using wind power is 27.3 m/sec. Interpret its meaning. show work. -------------- 75% of the sampled wind speeds were less than 27.3 m/sec. ================ Cheers, Stan H.
 Probability-and-statistics/315731: A student takes a multiple-choice quiz with four questions, each of which has four different answer choices (A, B, C, and D). Assume each question has one correct answer. Find the probability that the first two questions are answered correctly. 1 solutions Answer 225893 by stanbon(57307)   on 2010-06-19 13:14:04 (Show Source): You can put this solution on YOUR website!A student takes a multiple-choice quiz with four questions, each of which has four different answer choices (A, B, C, and D). Assume each question has one correct answer. Find the probability that the first two questions are answered correctly. --- P(1st correct) = 1/4 P(2nd correct) = 1/4 ---- P(1st two correct) = (1/4)^2 = 1/16 ==================================== Cheers, Stan H.
 Probability-and-statistics/315733: Determine whether the following events are independent or dependent. An urn contains three red tokens, five blue tokens, and two green tokens. A green token is drawn from the urn and is not replaced. A blue token is then drawn from the urn. 1 solutions Answer 225892 by stanbon(57307)   on 2010-06-19 13:10:32 (Show Source): You can put this solution on YOUR website!An urn contains three red tokens, five blue tokens, and two green tokens. A green token is drawn from the urn and is not replaced. A blue token is then drawn from the urn. -------------- The events are dependent because the green token was not replaced after it was drawn. --- P(blue) = 5/10 --- P(blue|green) = 5/9 --- Since P(blue) does not equal P(blue|green) the events are dependent. ================================ Cheers, Stan H. ================================