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Recent problems solved by 'stanbon'

stanbon answered: 57151 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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

percentage/269061: Evaluate the following given in the p/q form 23 1/3% 71 3/7% 63 2/4% 17 3/4% 7 3//6% 1 solutions Answer 197213 by stanbon(57219)   on 2010-02-12 22:17:06 (Show Source): You can put this solution on YOUR website! Evaluate the following given in the p/q form 23 1/3% = (3*23+1)/300 = 70/300 = 7/30 ---------------------------------------------- 71 3/7% = (7*71+3)/700 = 480/700 = 48/70 = 24/35 ---------------------------------------------- 63 2/4% = (4*63+2)/400 = 254/400 = 127/200 ---------------------------------------------- Etc. Cheers, Stan H. 17 3/4% 7 3//6%

Graphs/269068: The price P for a watermelon varies directly with its weight w. a) Write a formula for this variation. b) If the price of a 30-pound watermelon is $4.20, then what is the price of a 20-pound watermelon? 1 solutions Answer 197208 by stanbon(57219)   on 2010-02-12 22:05:45 (Show Source): You can put this solution on YOUR website! The price P for a watermelon varies directly with its weight w. a) Write a formula for this variation. P = kw ---------------------- b) If the price of a 30-pound watermelon is $4.20, Use that fact to find "k": 4.2 = k(30) k = 4.2/30 k = 2.1/15 k = 0.7/5 k = 7/50 So the Equation is P = (7/50)w ------------------------------------------- then what is the price of a 20-pound watermelon? P = (7/50)(20) P = 14/5 Price = $2.80 ================== Cheers, Stan H.

Distributive-associative-commutative-properties/269066: 25a squared-(a+5)squared 1 solutions Answer 197202 by stanbon(57219)   on 2010-02-12 21:54:46 (Show Source): You can put this solution on YOUR website! 25a squared-(a+5)squared (5a)^2 - (a+5)^2 ------------------ ---- Form: a^2-b^2 = (a-b)(a+b) -------------------------------- Your Problem: (5a - (a+5)(5a + (a+5) --- = (4a+5)(6a+5) ========================== Cheers, Stan H.

Functions/269041: How do you find the domain of f(x)=(x^2)ln(15-2(x^2)) 1 solutions Answer 197161 by stanbon(57219)   on 2010-02-12 20:00:30 (Show Source): You can put this solution on YOUR website! How do you find the domain of f(x)=(x^2)ln(15-2(x^2)) ---- You cannot find the ln of a negative number or zero, So, 15-2x^2 must be positive ---- Solve 15-2x^2 > 0 2x^2 < 15 x^2 < 15/2 -(15/2)sqrt(2) < x < (15/2)sqrt(2) --- Domain: All Real Numbers x where -(15/2)sqrt(2)< x < (15/2)sqrt(2) =================================================== Cheers, Stan H.

Functions/269042: How to solve (x-7/5)(x+5/7)? 1 solutions Answer 197159 by stanbon(57219)   on 2010-02-12 19:48:09 (Show Source): You can put this solution on YOUR website! How to solve (x-7/5)(x+5/7)? ---- General Form: (a-b)(a+b) = a^2 - b^2 ------ Your Problem: (x-7/5)(x+5/7) = x^2 - (25/49) =================== Cheers, Stan H.

Functions/269039: How do you find the domain of f(x)=9/(2+log(3x))? 1 solutions Answer 197158 by stanbon(57219)   on 2010-02-12 19:45:30 (Show Source): You can put this solution on YOUR website! find the domain of f(x)=9/(2+log(3x))? ---- Two conditions: 1. The denominator cannot be zero. 2. 3x must be >0 ----------------------------------- 1. Solve 2+log(3x) = 0 log(3x) = -2 3x = 10^-2 = 1/100 x = 1/300 ----------- 2. 3x > 0 x > 0 ------------- Domain: All Real Numbers >0 and not equal to 1/300. ===================================================== Cheers, Stan H.

Geometry_Word_Problems/269025: The lenght of a rectangle is 5cm more than 4 times it's width. The perimeter is 124cm find it's dimension? Find the modulas 1A multi and argument Z=3+6i Z=-3-4i Z=8-3i z=-6-3i 1 solutions Answer 197157 by stanbon(57219)   on 2010-02-12 19:35:37 (Show Source): You can put this solution on YOUR website! The length of a rectangle is 5cm more than 4 times it's width. The perimeter is 124cm find it's dimension? -------------- Perimeter = 2(width + length) 124 = 2(w + 4w+5) 62 = 5w+5 5w = 57 w = 57/5 w = 11 2/5 cm (width) length = 4w+5 = 4(57/5) + 5 = (228/5) + (25/5) = 253/5 = 50 3/5 cm (length) ========================== Find the modulas 1A multi and argument ----- Comment: One of those is the length; the other is the angle. I'll let you decide which is modulas and which as argument. ===================================== Z=3+6i length = sqrt(3^2 + 6^2) angle = arctan(6/3) = 63.43 degrees -------------------------------------- Z=-3-4i Note: This point is in the 3rd quadrant where tangents are positive but angles are between 180 and 270. --- length = sqrt(3^2 + 4^2) angle = arctan(-4/-3) = 53.13 degrees which is 180+53.13 = 233.13 ---------------------- Z=8-3i length = sqrt(8^2+3^2) angle is in QIV; arctan(-3/8)= -20.56 degrees ----------------------------------------- z=-6-3i I'll leave this one to you. ================================ Cheers, Stan H.

Miscellaneous_Word_Problems/269027: One serving of DietMuck is 2/3 of a cup. Jane wants to eat 2/3 of a serving of DietMuck. What fraction of a cup of DietMuck should Jane eat? a. Draw pictures to help you solve this problem b. In solving the problem, how does 2/3 appear in a different form? c. What are the different wholes associated with the fractions in this problem? In other words, for each fraction in this problem, and its solution, what is the fraction "of"? 1 solutions Answer 197152 by stanbon(57219)   on 2010-02-12 19:07:45 (Show Source): You can put this solution on YOUR website! One serving of DietMuck is 2/3 of a cup. Jane wants to eat 2/3 of a serving of DietMuck. What fraction of a cup of DietMuck should Jane eat? a. Draw pictures to help you solve this problem b. In solving the problem, how does 2/3 appear in a different form? c. What are the different wholes associated with the fractions in this problem? In other words, for each fraction in this problem, and its solution, what is the fraction "of"? ---- This is definitely a learning exercise. Try to take one step at a time following the a,b,c directions. The steps are self-explanatory; go for it. Cheers, Stan H.

Probability-and-statistics/269015: a couple has 4 children find the probability 3 are girls 1 solutions Answer 197151 by stanbon(57219)   on 2010-02-12 19:01:33 (Show Source): You can put this solution on YOUR website! a couple has 4 children find the probability 3 are girls ---- It's the same as the probability of having 1 boy. --- P(3 girls in 4) = 4C3(1/2)^3(1/2) = 4(1/2)^4 = 4(1/16) = 1/4 ======================= Cheers, Stan H.

Age_Word_Problems/269001: Twice my age now is the same as my age twenty years from now. Find my age now. 1 solutions Answer 197143 by stanbon(57219)   on 2010-02-12 17:08:39 (Show Source): You can put this solution on YOUR website! Twice my age now is the same as my age twenty years from now. Find my age now. ---- Let age now be "x". Equation: 2x = x+20 x = 20 ---------------- Cheers, Stan H.

Permutations/268998: There are six multiple-choice questions on an exam, each with three possible answers. Determine the number of possible answer sequences for the six questions 1 solutions Answer 197141 by stanbon(57219)   on 2010-02-12 17:05:12 (Show Source): You can put this solution on YOUR website! There are six multiple-choice questions on an exam, each with three possible answers. Determine the number of possible answer sequences for the six questions ------------ 1st question: 3 choices 2nd question: 3 choices --- --- 6th question: 3 choices ============================= Total # of possible sequences = 3^6 = 729 ============================================== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/268979: Two and more linear equations on the same plane form a ????? 1 solutions Answer 197128 by stanbon(57219)   on 2010-02-12 16:29:59 (Show Source): You can put this solution on YOUR website! Two parallel lines. OR Two lines that intersect at one point. OR Two lines that overlay one another. ======================================== Cheers, Stan H.

Equations/268378: factor the trinomial: 6r^2-60r+126 1 solutions Answer 197126 by stanbon(57219)   on 2010-02-12 16:21:21 (Show Source): You can put this solution on YOUR website! 6r^2-60r+126 ----- Common factor: 6 ---- = 6(r^2-10r+21) Think of two numbers whose product is 21 and whose sum is -10. The numbers are -7 and -3 Replace -10r by -7r-3r --- = 6(r^2-7r-3r+21) Factor the 1st 2 and the last 2 terms separately. --- = 6[(r(r-7)-3(r-7)] Factor again: = 6[(r-7)(r-3)] ===================== Cheers, Stan H.

Numbers_Word_Problems/268984: paul left springfield traveling north at an average speed of 64 miles per hour. tim left springfield traveling south at an avergae spped of 59 miles per hour. how long would it take after paul left for them to be 743 miles apart? how many hours would it be after paul left? 1 solutions Answer 197123 by stanbon(57219)   on 2010-02-12 16:09:22 (Show Source): You can put this solution on YOUR website! paul left springfield traveling north at an average speed of 64 miles per hour. tim left springfield traveling south at an avergae speed of 59 miles per hour. how long would it take after paul left for them to be 743 miles apart? how many hours would it be after paul left? --------------------------- They are separating at a rate of (64+59) = 123 mph --- time = distance/rate = 743/123 = 6.04 hrs (same time for both. --- Note: 0.04 hr = 0.04*60 minutes is approximately 3 minutes --- Ans: Approximate time = 6 hr. 3 minutes ============================================ Cheers, Stan H.

Sequences-and-series/268983: Insert K arithmetic means betweens the given numbers. 11/3 and 6; k=4 1 solutions Answer 197120 by stanbon(57219)   on 2010-02-12 16:01:36 (Show Source): You can put this solution on YOUR website! Insert K arithmetic means betweens the given numbers. 11/3 and 6; k=4 ---------------------- Difference = 6 - 11/3 = 18/3 - 11/3 = 7/3 ---- Solve 4x = 7/3 x = 7/12 ---- Sequence: 11/3 11/3 + 7/12 = 44/12 + 7/12 = 51/12 51/12 + 7/12 = 58/12 58/12 + 7/12 = 65/12 65/12 + 7/12 = 72/12 = 6 ===================================== Cheers, Stan H.

Equations/268981: one number is four times another. the sum of the numbers is 35. what are the numbers??? 1 solutions Answer 197118 by stanbon(57219)   on 2010-02-12 15:55:57 (Show Source): You can put this solution on YOUR website! one number is four times another. the sum of the numbers is 35. what are the numbers??? --------------- Number one: x Number two: 4x ------------------- Equation: x + 4x = 35 5x = 35 x = 7 4x = 28 ---------------- Cheers, Stan H.

Permutations/268980: How many improper subsets (including the set itself) are possible for the set (a,b,c,d)? 1 solutions Answer 197116 by stanbon(57219)   on 2010-02-12 15:54:03 (Show Source): You can put this solution on YOUR website! How many improper subsets (including the set itself) are possible for the set (a,b,c,d)? ---- Each subset either has or does not have a,b,c, or d. There are 2^4 choices. So there are 2^4 = 16 subsets including the set itself and the empty set. Cheers, Stan H.

Travel_Word_Problems/268968: At midnight car A is travling norht at 60 mph and is located 40 miles south of car B. Car B is travling West at 70 mph. Approximate the distance between the cars at 1:15 AM to the nearest tenth of a mile. I am not sure how to set this one up. I think its a right triangle however, only the hypotenuse is given if it is. All i was able to get is this: Rate Time Distance CarA 60 1.15 (not sure) CarB 70 1.15 (not sure) 1 solutions Answer 197073 by stanbon(57219)   on 2010-02-12 14:58:34 (Show Source): You can put this solution on YOUR website! At midnight car A is traveling north at 60 mph and is located 40 miles south of car B. Car B is travling West at 70 mph. Approximate the distance between the cars at 1:15 AM to the nearest tenth of a mile. I am not sure how to set this one up. I think its a right triangle however, only the hypotenuse is given if it is. All i was able to get is this: Rate Time Distance CarA 60 1.15 (not sure) CarB 70 1.15 (not sure) --------------------------- Draw a coordinate system. Put Car B at (0,0) Put Car A at (0,-40) ---- At 1:15 car A has gone time*rate = (5/4)(60)= 75 miles north and is then at point (0,35) --- In the same time car B has gone time*rate = (5/4)(70)= 87.5 miles and is then at point (-87.5,0) ---- Find the distance between (0,35) and (-87.5,0) I get 94.24 miles ======================== Cheers, Stan H.

Linear_Algebra/268962: Is there an example with Solving a linear equation with several occurrences of value. That may be shared in order to see ho the equation is done using fractions as well. Thanks 1 solutions Answer 197068 by stanbon(57219)   on 2010-02-12 14:46:16 (Show Source): You can put this solution on YOUR website! If you have any equation with fractions you can eliminate the fractions by multiply thru the equation by the least common multiple of the denominators. --------------------- Example: x/2 + 1/3 = y/5 --- lcm of 2,3,and 5 is 30 ---- Multiply thru by 30 to get: 15x + 10 = 6y Then: 6y = 15x+10 y = (15/6)x + (10/6) y = (5/2)x + (5/3) =========================== Hope that helps. Cheers, Stan H.

Quadratic_Equations/268967: Please help me solve this problem. 1. Type an exact answer, using radicals as needed. Rationalize all denominators. use a comma to seperate answeres as needed. 15x^4-8x^2+1=0 1 solutions Answer 197065 by stanbon(57219)   on 2010-02-12 14:40:53 (Show Source): You can put this solution on YOUR website! Type an exact answer, using radicals as needed. Rationalize all denominators. use a comma to seperate answeres as needed. 15x^4-8x^2+1=0 --- Think of two numbers whose product is 1*15 = 15 and whose sum is -8. The numbers are -5 and -3 --- Change the middle term of your problem to -5x-3x 15x^2-5x-3x+1 = 0 Factor the 1st 2 and the last two terms separately: 5x(3x-1)-(3x-1) = 0 Factor again: (3x-1)(5x-1) = 0 Solve for "x": x = 1/3 or x = 1/5 ========================== cheers, Stan H.

Travel_Word_Problems/268960: I throw a ball inot the air in a movie theater. I throw it up with an initial velocity of 64 feet/scecond froam a balcony 10 feet high. The ceiling of the theater is 58 feet high. When will the ball hit the ceiling/ 1 solutions Answer 197057 by stanbon(57219)   on 2010-02-12 14:10:20 (Show Source): You can put this solution on YOUR website! I throw a ball into the air in a movie theater. I throw it up with an initial velocity of 64 feet/sec1024ond from a balcony 10 feet high. The ceiling of the theater is 58 feet high. When will the ball hit the ceiling/ 000000000000000000 Height of the ball is h(t) = -16t^2+vot+so where vo is the initial velocity and so is the initial height. -------------- Your Problem: Solve 58 = -16t^2+64t+10 Rearrange: 16t^2 - 64t + 48 = 0 --- Factor: 16(t^2-4t + 3) = 0 16(t-3)(t-1) = 0 --- Smaller positive solution: t = 1 second The ball will hit the ceiling in one second. =========================================== Cheers, Stan H.

Inequalities/268952: 84+4x>8(x+9) the sign means greater then and equal to 4 x 1 solutions Answer 197048 by stanbon(57219)   on 2010-02-12 13:22:34 (Show Source): You can put this solution on YOUR website! 84+4x>8(x+9) 84 + 4x > 8x + 72 4x < 12 x < 3 ============ Cheers, Stan H.

Travel_Word_Problems/268946: Eruca hiked up a mountain trail at 3 km/hr and returned home at 4 km/hr. The entire trip took 5 hrs and 10 minutes. How long was the trail? 1 solutions Answer 197047 by stanbon(57219)   on 2010-02-12 13:20:54 (Show Source): You can put this solution on YOUR website! Eruca hiked up a mountain trail at 3 km/hr and returned home at 4 km/hr. The entire trip took 5 hrs and 10 minutes. How long was the trail? --- Up DATA: rate = 3 km/hr ; time = x hrs ; distance = 3x km --------------------- Down DATA: rate = 4 km/hr ; time = (5 1/6)-x hrs ; distance = 4[(31/6) -x] km =========================== Equation: distance up = distance down 3x = 4[(31/6)-x] 3x = (124/6) - 4x 7x = 124/6 x = 124/42 x = 2.95.. hrs --- Distance = 3x = 8.86.. km =========================== Cheers, Stan H.

Distributive-associative-commutative-properties/268950: Is it safe to say this is correct? I have problems with the signs. Please advise Thanking you in advance 5(x -2)+2 = 2(3x +3) +3x = 5x -10 +2 = 6x +6 +3 = 5x -8 = 18x +6 = 5x +18x +6 = 5x +18x = 6-8 = 23x = -2 x = -2/23 1 solutions Answer 197046 by stanbon(57219)   on 2010-02-12 13:13:24 (Show Source): You can put this solution on YOUR website! 5(x -2)+2 = 2(3x +3) +3x 5x -10 +2 = 6x +6 +3x 5x -8 = 9x +6 Add 8 to both sides: Subtract 9x from both sides: -4x = 14 x = -14/4 x = -7/2 ================ Note: I have corrected it. ================ Cheers, Stan H.

Triangles/268945: Find the fourth term in the following recursively defined sequence. a1 = 2 an = an-1 + 3 1 solutions Answer 197045 by stanbon(57219)   on 2010-02-12 13:09:03 (Show Source): You can put this solution on YOUR website! Find the fourth term in the following recursively defined sequence. a1 = 2 an = an-1 + 3 -------------------- a1 = 2 a2 = 2+3 = 5 a3 = 5+3 = 8 a4 = 8+3 = 11 ==================' Cheers, Stan H.

Probability-and-statistics/268871: a financial analyst believes that if interest rate decrease in a given period, then the probability that the stock market will go up is 0.80. the analyst further believes that interest rates have a 0.40 chance of decreasing during the period in question. given the above information, what is the probability that the market will go up and interest rate go down during the period in question. 1 solutions Answer 197043 by stanbon(57219)   on 2010-02-12 13:06:27 (Show Source): You can put this solution on YOUR website! a financial analyst believes that if interest rate decrease in a given period, then the probability that the stock market will go up is 0.80. the analyst further believes that interest rates have a 0.40 chance of decreasing during the period in question. given the above information, -------------------- what is the probability that the market will go up and interest rate go down during the period in question. Prob(market up) = 0.8 Prob(interest down) = 0.40 ---- P(m up and i down) = 0.8*0.4 = 0.32 ====================================== Cheers, Stan H.

Probability-and-statistics/268918: In the 108th Congress, the Senate consists of 51 Republicans, 48 Democrats, and 1 independant. If a lobbyist for the tobacco industry randomly selects 3 different Senators, what is the probability that they are all Republicans? Would a lobbyist by likely to use random selection in this situation? 1 solutions Answer 197041 by stanbon(57219)   on 2010-02-12 13:02:23 (Show Source): You can put this solution on YOUR website! In the 108th Congress, the Senate consists of 51 Republicans, 48 Democrats, and 1 independant. If a lobbyist for the tobacco industry randomly selects 3 different Senators, what is probability that they are all Republicans = 51C3/100C3 = 0.1288 ------------------------------------ Would a lobbyist by likely to use random selection in this situation? No -------------- Cheers, Stan H.

logarithm/268907: write each equation so it contains no logarithms 1. log x + 3 log y = 0 2. 2 ln (x-1) = 5 ln (y+2) 1 solutions Answer 197021 by stanbon(57219)   on 2010-02-12 11:16:04 (Show Source): You can put this solution on YOUR website! write each equation so it contains no logarithms 1. log x + 3 log y = 0 --- log(x) + log(y^3) = 0 --- log(xy^3) = 0 xy^3 = 10^0 xy^3 = 1 ------------------ 2. 2 ln (x-1) = 5 ln (y+2) --- ln(x-1)^2 = ln(y+2)^5 ----- (x-1)^2 = (y+2)^5 ======================== cheers, Stan H.

Complex_Numbers/268901: How can I solve this equation for b?.... i/a+i/b=3/c Please show steps 1 solutions Answer 197020 by stanbon(57219)   on 2010-02-12 11:12:06 (Show Source): You can put this solution on YOUR website! solve this equation for b?.... i/a+i/b=3/c --- Subtract i/a from both sides --- i/b = 3/c-(i/a) --- Simplify the right side: i/b = (3a-ic)/(ac) --- Invert both sides: b/i = (ac)/(3a-ic) --- Multiply both sides by "i": b = (aci)/(3a-ic) ============================ Cheers, Stan H.

Rational-functions/268902: Solve. q=p-np, Solve for P 1 solutions Answer 197018 by stanbon(57219)   on 2010-02-12 11:05:33 (Show Source): You can put this solution on YOUR website! q=p-np, Solve for P --- Factor the right side: q = p(1-n) Divide both sides by 1-n to get: p = q(1-n) ================== Cheers, Stan H.

Probability-and-statistics/268868: a certain operation on a time- shared computer takes anywhere from 1/100 to 4/100 of a second, and the operation time is no more likely to be in any sub interval in this range than it is to be in any other sub interval of the same length. what is the probability that the operation will take over 2/100 of a second? 1 solutions Answer 197017 by stanbon(57219)   on 2010-02-12 11:03:44 (Show Source): You can put this solution on YOUR website! a certain operation on a time- shared computer takes anywhere from 1/100 to 4/100 of a second, and the operation time is no more likely to be in any sub interval in this range than it is to be in any other sub interval of the same length. what is the probability that the operation will take over 2/100 of a second? ----------- Assuming the times are normally distributed: mean = [(4-1)/100]/2 = (1.5)/100 = 0.015 --- Assume the data range is 6sigma wide Then 6sigma = 3/100 sigma = 0.5/100 = 0.005 ------- z(2/100) = (0.020-0.015)/0.005 = 0.005/0.005 = 1 ---- P(x > 0.02) = P(z > 1) = 0.1587.. ================================= Cheers, Stan H.