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Recent problems solved by 'stanbon'

stanbon answered: 57894 problems
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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Square-cubic-other-roots/687514: Hi! How would I solve the square root of a number when there's another number on the outside of the square root? For example, the example is asking me to find the decimal expression of the square root of 64, which I know is 8, but then it has the number 4 on the outside of the square root? I'm not sure what to do with the 4. Thank you! 1 solutions Answer 425179 by stanbon(57967)   on 2012-11-30 09:55:31 (Show Source): You can put this solution on YOUR website! How would I solve the square root of a number when there's another number on the outside of the square root? For example, the example is asking me to find the decimal expression of the square root of 64, which I know is 8, but then it has the number 4 on the outside of the square root? I'm not sure what to do with the 4. Thank you! -------------------- 4*sqrt(64) = 4*8 = 32 --- If the "4" is small and indicates "take the 4th root", the answer would be: 4th root of (64) = 4th root of 2^6 = 2^(6/4) = 2^(3/2) ========================================================== Cheers, Stan H. ===========================

Age_Word_Problems/687506: Paul is 7 years older than his brother. The product of their ages is 30. How old is Paul? 1 solutions Answer 425178 by stanbon(57967)   on 2012-11-30 09:49:03 (Show Source): You can put this solution on YOUR website! Paul is 7 years older than his brother. The product of their ages is 30. How old is Paul? --------------- Equations:' p = b + 7 p*b = 30 ---- Substitute for "p" and solve for "b": (b+7)b = 30 b^2 + 7b = 30 b^2 + 7b - 30 = 0 Factor: b^2 + 10b-3b - 30 = 0 ------- b(b+10) -3(b+10) = 0 (b+10)(b-3) = 0 Positive solution: b = 3 yrs. (brother's age) p = b+7 = 10 yrs (Paul's age) ================= Cheers, Stan H. =================

Triangles/687504: how many different right triangles have at least one angle that measures exactly 20 degrees 1 solutions Answer 425177 by stanbon(57967)   on 2012-11-30 09:40:19 (Show Source): You can put this solution on YOUR website! how many different right triangles have at least one angle that measures exactly 20 degrees ----- Ans: An infinite number. Cheers, Stan H. =========

logarithm/687214: x^log2(x)=16x^3 that is log base 2 of x (to clarify) solve for x 1 solutions Answer 425176 by stanbon(57967)   on 2012-11-30 09:33:52 (Show Source): You can put this solution on YOUR website! x^log2(x)=16x^3 ------ Graph and find the intersection. ---- Ans: x = 1/2 ------------------- Cheers, Stan H. ===================

logarithm/687247: How do I express this as a single logarithm? 3/2ln (4y^2)-4/5ln 2m^10 1 solutions Answer 425174 by stanbon(57967)   on 2012-11-30 09:15:25 (Show Source): You can put this solution on YOUR website! express this as a single logarithm? (3/2)ln (4y^2)-(4/5)ln (2m)^10) --------- = ln[(4y^2)^(3/2)] - ln[(2m)^10)^(4/5)] ----- = ln[8y^3] - ln[(2m)^8] ---- = ln[8y^3 - ln[256m^8] ----- = ln[y^3/32m^8] =================== Cheers, Stan H. ===================

logarithm/687355: write in single logarithm 1/5[3log(x+1)+2log(x-1)-log7] 1 solutions Answer 425173 by stanbon(57967)   on 2012-11-30 09:07:08 (Show Source): You can put this solution on YOUR website! write in single logarithm 1/5[3log(x+1)+2log(x-1)-log7] ----- = log[(x+1)^3*(x-1)^2/7]^(1/5) ============================ Cheers, Stan H.

logarithm/687488: In the following practice example Im confused, I think the first and third are true but I am not sure Im doing it right at all. Confused. Which of the following statements is true, or are none of them true? ln(x-2) = ln x - ln 2 ln(x-2) = x - ln 2 ln(x-2) = ln(x/2) <- x/2 written as fraction 1 solutions Answer 425172 by stanbon(57967)   on 2012-11-30 09:05:28 (Show Source): You can put this solution on YOUR website! Which of the following statements is true, or are none of them true? ln(x-2) = ln x - ln 2:::::: false ln(x-2) = x - ln 2:::::false ln(x-2) = ln(x/2) <- x/2 written as fraction ::: false ------------- Cheers, Stan H. ==========

logarithm/687487: Solve 3^x-1=7 Write 6log4x+log4y as a single logarithm Solve. 3^2x-1 x 81^2/4 __________________ = 9^5x 27^1-x 1 solutions Answer 425171 by stanbon(57967)   on 2012-11-30 09:02:48 (Show Source): You can put this solution on YOUR website! Solve 3^x-1=7 3^(x-1) = 7 (x-1)*log(3) = log(7) ----- x*log(3) = log(3)+log(7) x = log(21)/log(3) x = 2.77 ------------------------- Write 6log4x+log4y as a single logarithm 6*log4(x) + log4(y) --- = log4(x^6)+log4(y) --- = log4[x^6*y] ====================== Solve. 3^2x-1 x 81^2/4 __________________ = 9^5x 27^1-x -------------- [3^(2x-1)*(3^4)^(2/4)]/(3^3)^(1-x) = (3^2)^5x ----------------- [(3)^(2x-1)*(3^2)]/3^(3-3x) = 3^10x ----------------- [3^(2x+1)/3^(3-3x)] = 3^10x ------------------ [3^(5x-2)] = 3^10x ----- 5x-2 = 10x 5x = -2 x = -2/5 =========== Cheers, Stan H. =============

Angles/687485: what angle measure is complementary to a 22 degree angle. 1 solutions Answer 425168 by stanbon(57967)   on 2012-11-30 08:45:53 (Show Source): You can put this solution on YOUR website! what angle measure is complementary to a 22 degree angle. ---- Equation: x + 22 = 90 x = 90-22 x = 68 degrees ------------ Cheers, Stan H. =============

Linear-equations/687473: graph the equation using the x and y intercepts x/2 - x/9 = 1 1 solutions Answer 425167 by stanbon(57967)   on 2012-11-30 08:44:26 (Show Source): You can put this solution on YOUR website! graph the equation using the x and y intercepts x/2 - y/9 = 1 ----- If x = 0, y = -9 If y = 0, x = 2 ---- Plot (0,-9) and (2,0) and draw a line thru them. Cheers, Stan H. ============

Problems-with-consecutive-odd-even-integers/687482: The sum of the larger of two consecutive numbers and five times the smaller one is 187. What is the smallest of the integers? 1 solutions Answer 425166 by stanbon(57967)   on 2012-11-30 08:40:24 (Show Source): You can put this solution on YOUR website! answered

Problems-with-consecutive-odd-even-integers/687476: Classify the following as an example of a nominal, ordinal, interval, or ratio level of measurement, and state why it represents this level: gender of employees at a local warehouse can some one walk me through this 1 solutions Answer 425165 by stanbon(57967)   on 2012-11-30 08:39:01 (Show Source): You can put this solution on YOUR website! Classify the following as an example of a nominal, ordinal, interval, or ratio level of measurement, and state why it represents this level: gender of employees at a local warehouse ----- gender is a naming word so it's nominal. Cheers, Stan H.

Problems-with-consecutive-odd-even-integers/687481: The sum of the larger of two consecutive numbers and five times the smaller one is 187. What is the smallest of the integers? 1 solutions Answer 425164 by stanbon(57967)   on 2012-11-30 08:36:24 (Show Source): You can put this solution on YOUR website! The sum of the larger of two consecutive numbers and five times the smaller one is 187. What is the smallest of the integers? ----- 1st: x 2nd: x+1 --- Eqution: (x+1) + 5x = 187 6x = 186 x = 31 ------------- Cheers, Stan H.

Problems-with-consecutive-odd-even-integers/687477: Classify the following variable as nominal, ordinal, discrete, or continuous and state why it is such a variable: weight of a textbook can someone walk me through this 1 solutions Answer 425163 by stanbon(57967)   on 2012-11-30 08:34:18 (Show Source): You can put this solution on YOUR website! Classify the following variable as nominal, ordinal, discrete, or continuous and state why it is such a variable: weight of a textbook ------ It's not a name so it's not nomial It's not the order of something, so it's not ordiinal It's not an exact value (weights can vary depending on the weighing instrument) so it's not discrete. --- It's continuous. Cheers, Stan H. ===============

Probability-and-statistics/687161: Of randomly selected students with random variable x with normal distribution. 12.10% score below 60 and 6.3% score above 95. I have to find µ = E[X] and σ^2 = Variance (X). I have no idea what to do with this at all please help. 1 solutions Answer 425121 by stanbon(57967)   on 2012-11-29 21:10:26 (Show Source): You can put this solution on YOUR website! Of randomly selected students with random variable x with normal distribution. Draw a normal curve. 12.10% score below 60 and 6.3% score above 95. sketch a left-tail of 12.10% to the left of 60 Find the z-value with that left tail: invNorm(0.121) = -1.17 ----- sketch a right-tail of 6.3% to the right of 95 Find the z-value with a left tail of 93.7% invNorm(0.937) = 1.53 -------- I have to find µ = E[X] and σ^2 = Variance (X). ---- Form 2 equations using x = z*s + u to solve for s and u: 60 = -1.17*s + u 95 = 1.53*s + u ------ Subtract to solve for "s": 35 = 2.7s s = 12.96 Variance = s^2 = 168 ------ Solve for "u" using 60 = -1.17s + u 60 = -1.17*12.96 + u u = 75.163 ======================= Cheers, Stan H.

Probability-and-statistics/687323: Can someone please help me with this problem? This select group has been asked to consider the Colorado City Convention and Visitors Bureau survey of 25 hotels in the local area. The survey is concerned with the current availability of rooms. The availability of the rooms was as follows: 90, 72, 75, 60, 75, 72, 84, 72, 88, 74, 105, 115, 68, 74, 80, 64, 414, 82, 48, 58, 60, 80, 48, 58, and 108. Consider the average available for all hotel rooms, and identify the point estimate of the average number of available hotel rooms in this lesson from each sample. Construct and interpret a 95 percent confidence level for the true mean number of available hotel rooms, based on the point estimate of each sample. Describe how the confidence intervals will change depending on whether the population standard deviation is known or unknown. 1 solutions Answer 425116 by stanbon(57967)   on 2012-11-29 20:56:06 (Show Source): You can put this solution on YOUR website! This select group has been asked to consider the Colorado City Convention and Visitors Bureau survey of 25 hotels in the local area. The survey is concerned with the current availability of rooms. The availability of the rooms was as follows: 90, 72, 75, 60, 75, 72, 84, 72, 88, 74, 105, 115, 68, 74, 80, 64, 414, 82, 48, 58, 60, 80, 48, 58, and 108. Consider the average available for all hotel rooms, and identify the point estimate of the average number of available hotel rooms in this lesson from each sample. --- Assuming you posted your data values correctly, There appears to be only one sample. --- x-bar = 89.54 ---- std of the sample = 71.23 = 14.246 ------- Construct and interpret a 95 percent confidence level for the true mean number of available hotel rooms, based on the point estimate of each sample. ME = 1.96*71.23/sqrt(5) = 1.96*14.246 = 27.92 ---- 95% CI: 89.54-27.92 < u < 89.54+27.92 ======================================== Describe how the confidence intervals will change depending on whether the population standard deviation is known or unknown. ---- I'll leave that to you. ------- Cheers, Stan H.

Distributive-associative-commutative-properties/687320: How do you solve: -3+2c<5c+7<23+3c? 1 solutions Answer 425115 by stanbon(57967)   on 2012-11-29 20:43:55 (Show Source): You can put this solution on YOUR website! -3+2c <5c+7< 23+3c --------------------- Separate the pieces: -3+2c < 5c+7 -10 < 3c c > -10/3 ------ 5c+7 < 23+3c 2c < 16 c < 8 ---- Combine the answers: -10/3 < c < 8 =================== cheers, Stan H. ==================

Graphs/687311: I have a test tomorrow, I have no clue how to graph this: Solve the system graphically: -3x + y = 7 -4x +4y +12 I got this so far : y + 3x + 7 y = x + 3 Then they want me to graph it. Everyone tries to tell help me, but only makes it more confusing. 1 solutions Answer 425113 by stanbon(57967)   on 2012-11-29 20:37:34 (Show Source): You can put this solution on YOUR website! Solve the system graphically: -3x + y = 7 -4x +4y = 12 ----- Graph the 1st equation y = 3x + 7 If x = 0, y = 7 If x = 1, y = 10 ---- Plot (0,7) and (1,10) and draw a line thru them. ==================================================== Graph the 2nd equation: !st simplify by dividing thru by -4 to get: x - y = -3 2nd: Solve for "y": y = x+3 --- If x = 0, y = 3 If x = 1, y = 4 ---- Plot (0,3) and (1,4) and draw a line thru them. ------ ----------------- Solution is the point of intersection of the 2 lines: (-2,1) ================== Cheers, Stan H.

Linear-systems/687304: Please help me solve this: 3x-y=11 x+y=5 in elimination and substitution method. 1 solutions Answer 425108 by stanbon(57967)   on 2012-11-29 20:29:40 (Show Source): You can put this solution on YOUR website! 3x-y=11 x+y=5 in elimination and substitution method. ------------------------- Elimination: 3x-y =11 x +y =5 ----- Add and solve for "x": 4x = 16 x = 4 ---- Solve for "y" using x + y = 5 4 + y = 5 y = 1 --------- Substitution: 3x-y =11 x +y =5 ----- Solve the bottom equation for "x": x = 5-y Substitute into the top equation to solve for "y": 3(5-y) - y = 11 15 - 3y -y = 11 -4y = -4 y = 1 ---- solve for "x" using x = 5-y x = 5-1 = 4 ==================== cheers, Stan H. ========================

Quadratic_Equations/687298: I have the vertex (2,-3) and one point (-1,3) I need to write a quadic formula also I have the vertex (-1,6) and the y intercept =3 and I have to write a quadric formula for that also. Can you tell me the steps to writing a formula from this information? Thank you! 1 solutions Answer 425106 by stanbon(57967)   on 2012-11-29 20:22:22 (Show Source): You can put this solution on YOUR website! I have the vertex (2,-3) and one point (-1,3) I need to write a quadratic formula ----- Form: y = a(x-h)^2+k where (h,k) is the vertex --- Using the vertex and the point, solve for "a": 3 = a(-1-2)^2-3 6 = a(9) a = 2/3 ----- Equation: y = (2/3)(x-2)^2 -3 --- y = (2/3)(x^2-4x+4) - 3 --- y = (2/3)x^2 - (8/3)x - 1/3 ================================== also I have the vertex (-1,6) and the y intercept =3 and I have to write a quadratic formula for that also. Using the same form: vertex (-1,6) ; point (0,3) ------ y = a(x-h)^2 + k 3 = a(0--1)^2 + 6 3 = a(1)+6 a = -3 ---- Equation: y = -3(x+1)^2 +6 ---- y = -3(x^2+2x+1) + 6 ---- y = -3x^2 -6x + 3 ========================= Cheers, Stan H. ==================

Percentage-and-ratio-word-problems/687300: this is not a word problem just a fraction problem. the math problem is 2 5/8 TIMES 6 2/3 ( two and fife eights times 6 and two thirds ) i dont need an explanation, because i will be able to figure it out on my own. all i need is the answer because my math teacher is making me do it a certain way so it would be a little pointless for you to explain it! thank you very much! :) 1 solutions Answer 425105 by stanbon(57967)   on 2012-11-29 20:09:41 (Show Source): You can put this solution on YOUR website! 2 5/8 TIMES 6 2/3 -------- = (21/8)(20/3) ---- Reduce the fractions: = (7/2)(5/1) ----- = 35/2 ---- = 17 1/2 ===================== Cheers, Stan H. ======================

test/687288: find the roots of the polynomial equation 2x^4-5x^3-17x^2+41x-21=0 1 solutions Answer 425103 by stanbon(57967)   on 2012-11-29 20:07:13 (Show Source): You can put this solution on YOUR website! find the roots of the polynomial equation 2x^4-5x^3-17x^2+41x-21=0 ----- The coefficients add up to zero, so x = 1 is a root. --- Use synthetic division to find other roots: ----- 1)....2....-5....-17....41....-21 ......2....-3....-20....21....|..0 --------------------- Again the coefficients add up to zero, so x = 1 is again a root: ---- 1)....2....-3....-20....21 ......2....-1....-21...|..0 Quotient: 2x^2 -x -21 ----- Factor: 2x^2 -7x+6x -21 = 0 x(2x-7 + 3(2x-7) = 0 (2x-7)(x+3) = 0 Roots: x = 7/6, x = -3, x = 1 (multiplicity 2) =========================== Cheers, Stan H. ===========================

Linear-equations/687293: A certain mountain has an elevation of 19,785ft. In 1919, the glacier on this peak covered 10 acres. By 2003, this glacier has melted to 1 acre. The yearly rate of change is ___ acres/year. What is the equation that gives the acreage of the glacier (t) years after 1919? Any help would be appeaciated. Thanks 1 solutions Answer 425100 by stanbon(57967)   on 2012-11-29 19:58:22 (Show Source): You can put this solution on YOUR website! A certain mountain has an elevation of 19,785ft. In 1919, the glacier on this peak covered 10 acres. By 2003, this glacier has melted to 1 acre. The yearly rate of change is ___ acres/year. What is the equation that gives the acreage of the glacier (t) years after 1919? Any help would be appeaciated. ---- You have 2 points relating year after 1919 and acreage: (0,10) and (3,1) ----- slope = (1-10)/(3-0) = -3 --- intercept = G(0) = 10 ---------------------------- Equation: G(t) = -3t + 10 ===================== Cheers, Stan H. =====================

Coordinate-system/687291: Find the value of x so that the points lie on a line with the given slope. (x,2) and (-5,8), m= -1 When I solve this I get the answer as -4.83. Is this correct? 1 solutions Answer 425099 by stanbon(57967)   on 2012-11-29 19:54:32 (Show Source): You can put this solution on YOUR website! Find the value of x so that the points lie on a line with the given slope. (x,2) and (-5,8), m= -1 ---- Equation: (8-2)/(-5-x) = -1 ----- 6/(5+x) = 1 5+x = 6 x = 1 -------------------- Cheers, Stan H.

Percentage-and-ratio-word-problems/687290: if the total is 450 what is 1 out of 5 1 solutions Answer 425098 by stanbon(57967)   on 2012-11-29 19:50:46 (Show Source): You can put this solution on YOUR website! if the total is 450 what is 1 out of 5 ---- Equation: x/450 = 1/5 x = 450(1/5) = 90 ===================== Cheers, Stan H.

Probability-and-statistics/687089: Variables such as height and weight are generally assumed to be normally distributed (for example, population data would take the shape of a normal curve). Discuss at least two samples in which you would not expect this to be true. Make sure you explain how the shape of the curve would differ from the norm and why it would differ. 1 solutions Answer 425016 by stanbon(57967)   on 2012-11-29 14:53:45 (Show Source): You can put this solution on YOUR website! Variables such as height and weight are generally assumed to be normally distributed (for example, population data would take the shape of a normal curve). Discuss at least two samples in which you would not expect this to be true. Make sure you explain how the shape of the curve would differ from the norm and why it would differ. ----- Variables such as time and height of a baseball above the ground would have the shape of a parabola opening downward. ---- Variables such as salary and age would be skewed to the right. ----------------- Cheers, Stan H.

Probability-and-statistics/687062: Some material is placed in a store with variable humidity,resulting in various degrees of wetness of the material.Both humidity and moisture content are measured as percentages with the following results: Humidity,x: 42 35 50 43 48 62 31 Moisture content,y: 2 8 14 9 11 16 7 Use the method of least squares to find a regression line, and use this line to estimate the moisture content when the humidity is 55%.Give a 95% Confidence interval for this estimate. I am trying to solve it for many days now,but I cannot. Thank you. 1 solutions Answer 425014 by stanbon(57967)   on 2012-11-29 14:49:18 (Show Source): You can put this solution on YOUR website! Some material is placed in a store with variable humidity,resulting in various degrees of wetness of the material.Both humidity and moisture content are measured as percentages with the following results: Humidity,x: 42 35 50 43 48 62 31 Moisture content,y: 2 8 14 9 11 16 7 -------------------- Use the method of least squares to find a regression line, and use this line to estimate the moisture content when the humidity is 55%. --- I used the linear regression function on my TI-84 to get: y = 0.34x - 5.34 ----- f(55) = 13.118 ================ Give a 95% Confidence interval for this estimate. I'll leave this to you. Cheers, Stan H. ===============

Probability-and-statistics/687083: Membership in an elite oraganization requires a test score in the upper 30% range. If the mean is 115 and the standard deviation is 12,find the lowest acceptable score that would enable a candidate to apply for membership. Assume the variable is normally distributed. 1 solutions Answer 425013 by stanbon(57967)   on 2012-11-29 14:43:20 (Show Source): You can put this solution on YOUR website! Membership in an elite oraganization requires a test score in the upper 30% range. If the mean is 115 and the standard deviation is 12,find the lowest acceptable score that would enable a candidate to apply for membership. Assume the variable is normally distributed. ==== Find the z-score with a left-tail 0 70%. invNorm(0.70) = 0.5244 ---- Find the corresponding test score using x = z*s + u x = 0.5244*12 + 115 = 121.29 ====================== Cheers, Stan H.

Probability-and-statistics/687042: membership in an elite organization requires a test score in the upper 30% range. if the mean is 115 and the standard deviation is 12, find the lowest acceptable score that would enable a candidate to apply for membership. assume the variable is normally distributed. 1 solutions Answer 424998 by stanbon(57967)   on 2012-11-29 13:19:15 (Show Source): You can put this solution on YOUR website! membership in an elite organization requires a test score in the upper 30% range. if the mean is 115 and the standard deviation is 12, find the lowest acceptable score that would enable a candidate to apply for membership. assume the variable is normally distributed. ------- Use the form x = z*s+u ---- Find the z-value with a left-tail of 0.70 invNorm(0.70) = 0.5244 ---------------------------- x = 0.5244*12 + 115 x = 121.29 ===================== Cheers, Stan H.

Probability-and-statistics/687044: On the daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is normally distributed. Find the probability that the bus will have between 36 and 40 passengers. 1 solutions Answer 424997 by stanbon(57967)   on 2012-11-29 13:12:36 (Show Source): You can put this solution on YOUR website! On the daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is normally distributed. Find the probability that the bus will have between 36 and 40 passengers. ----- Find the z-values for 36 and for 40. Find the probability that z lies between those two z-values. ================= Using a TI-84 I get P(36<= x <=40) = 0.0038 ==================== Cheers, Stan H.

Probability-and-statistics/686885: I made 20 measurements of friction on one type of material with average result of friction 30,5 % and another 20 measurement of friction on second type of material with average result of 35,5 %. Now I would like to know, whether this difference is significant, using alpha 0,05. Please, could you help? Many thanks. 1 solutions Answer 424996 by stanbon(57967)   on 2012-11-29 13:09:17 (Show Source): You can put this solution on YOUR website! I made 20 measurements of friction on one type of material with average result of friction 30,5 % and another 20 measurement of friction on second type of material with average result of 35,5 %. Now I would like to know, whether this difference is significant, using alpha 0,05. Please, could you help? ------ Ho: p1-p2 = 0 Ha: p1-p2 # 0 ------ test statistic: z = (0.305-0.355)/sqrt[(0.305*0.695/20) + (0.355*0.645/20)] = -0.05/0.1485 = -0.3367 ----- Critical values for 2-tail test with alpha = 5%: +-1.96 ----- Conclusion: Since the test stat is not in the reject interval, fail to reject Ho. There is no significant difference at the 5% level. Cheers, Stan H.