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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>Next

Mixture_Word_Problems/481640: If you have 70mL of 35% solution of acid in water, how much water would you add in order to make a 25% acid solution? 1 solutions Answer 329772 by stanbon(57967)   on 2011-08-14 20:03:21 (Show Source): You can put this solution on YOUR website! If you have 70mL of 35% solution of acid in water, how much water would you add in order to make a 25% acid solution? ------------------------------------------ Equation: acid + acid = acid 0.35*70 + 0*x = 0.25(70+x) ---- Multiply thru by 100 to get: 35*70 + 0 = 25*70+25x ----- 25x = 10*70 ---- x = 28mL (amt. of water needed) ======================= Cheers, Stan H.

Equations/481587: I need help please.. Short Answer: Simplify the following expression, and rewrite it in an equivalent form with positive exponents. (5x^-1)^-3 1 solutions Answer 329722 by stanbon(57967)   on 2011-08-14 17:29:47 (Show Source): You can put this solution on YOUR website! Simplify the following expression, and rewrite it in an equivalent form with positive exponents. (5x^-1)^-3 ------ = (1/125)x^3 ================= Cheers, Stan H.

Equations/481588: I have no idea what to do, can someone help? Short Answer: Simplify the following expression; express in terms of i. square root -144 1 solutions Answer 329721 by stanbon(57967)   on 2011-08-14 17:26:47 (Show Source): You can put this solution on YOUR website! Simplify the following expression; express in terms of i. square root -144 ---- sqrt(-144) = 12i ==================== Cheers, Stan H.

Probability-and-statistics/481422: - 42% teen smoke cigarettes - 53% of all smokers are female - 45% of all non-smoker are female - What the probability of selecting a female, and she doesn’t smoke 1 solutions Answer 329668 by stanbon(57967)   on 2011-08-14 10:43:26 (Show Source): You can put this solution on YOUR website! - 42% teen smoke cigarette - 53% of all smokers are female - 45% of all non-smoker are female - What the probability of selecting a female, and she doesn’t smoke ----------------- 58% of teens do not smoke 45% of those are female ---- 0.45*0.58 = 0.2610 is the probability of selecting a female that does not smoke ======== Cheers, Stan H.

Probability-and-statistics/481448: Given a binomial distribution with n = 23 and p = 0.78, would the normal distribution provide a reasonable approximation? Why or why not? Thank you 1 solutions Answer 329667 by stanbon(57967)   on 2011-08-14 10:29:27 (Show Source): You can put this solution on YOUR website! Various texts have varying criteria for this. Please check your text. ---- If that doesn't work try Google for "normal approximation criteria". Cheers, Stan H.

Probability-and-statistics/481450: Find the value of z such that approximately 13.68% of the distribution lies between it and the mean. Thanks 1 solutions Answer 329666 by stanbon(57967)   on 2011-08-14 10:26:59 (Show Source): You can put this solution on YOUR website! Find the value of z such that approximately 13.68% of the distribution lies between it and the mean. --- 1st: Draw the picture so you can see what you are calculating. 2nd: 0.5000-0.1368 = 0.3632 3rd: Find the z-value with a left-tail of 0.3632 using z = invNorm(0.3632) = -0.3499 4th: By symmetry, +0.3499 is also a solution. ===================== Cheers, Stan H.

Probability-and-statistics/481453: Answer the following: (A) Find the binomial probability P(x = 5), where n = 14 and p = 0.70. (B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation. (C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations Thanks 1 solutions Answer 329663 by stanbon(57967)   on 2011-08-14 10:22:02 (Show Source): You can put this solution on YOUR website! Answer the following: (A) Find the binomial probability P(x = 5), where n = 14 and p = 0.70. Ans: 14C5(0.7)^5(0.3)^9 = binompdf(14,0.7,5) = 0.00660.7746 ------------------------------ (B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation. P(0<= x <=5) = 14C0(0.7)^0*(0.3)^14+14C1(0.7)*(0.3)^13+ etc. ------------------------- (C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations u = np = 14*0.7 = 2 s = sqrt(npq) = sqrt(2*0.3) = 0.7746 --------------- binomial probability (x = 5) equals normal approximation probability (4.5 < x < 5.5) ============ Cheers, Stan H. ===========

Probability-and-statistics/481260: Hypothesis Test- (1 sample/2 Tail) Conduct a 7-step Hypothesis Test to determine if the year-end bonus is different from the reported mean. Known Information: u= 125500 x with line over top= 118000 s= 30000 n= 40 I need to see the 7 steps on paper and how you would figure that on Excel. 1 solutions Answer 329607 by stanbon(57967)   on 2011-08-13 21:44:19 (Show Source): You can put this solution on YOUR website! Conduct a 7-step Hypothesis Test to determine if the year-end bonus is different from the reported mean. Known Information: u= 125500 x with line over top= 118000 s= 30000 n= 40 --------------- Ho: u = 125500 H1: u is not equal to 125500 ------------------ test statistic: t = (118000-125500)/[30000/sqrt(40)] = -1.5811 ---- To draw a conclusion you can compare the test statistic to the critcal value for a t-test or you can use the p-value comparison. ---- Since yours is a 2-tail test, p-value = 2*P(t < -1.5811 when df = 39) = 2*tcdf(-100,-1.5811,39) = 0.1219 Note: I used a TI-84 to find the probability that t was less then -1.5811 when df = 39. Then I doubled it because of the 2-tail feature. Hope this helps. If it doesn't make any sense, use the critical value test. ============= Conclusion: Since the p-value is greater than 5% fail to reject Ho. =================== Cheers, Stan H. =====================

Probability-and-statistics/481265: An automobile assembly line operation has a scheduled mean completion time of 14.7 minutes. The standard deviation of completion times is 1.7 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 80 completion times under new management was taken. The sample had a mean of 14.2 minutes. Can we support, at the 0.01 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed. The value of the test statistic (round to at least 3 decicmal places)? The p-value(round to at least 3 decimal places)? 1 solutions Answer 329601 by stanbon(57967)   on 2011-08-13 21:30:54 (Show Source): You can put this solution on YOUR website! An automobile assembly line operation has a scheduled mean completion time of 14.7 minutes. The standard deviation of completion times is 1.7 minutes. ----------------------------------- It is claimed that, under new management, the mean completion time has decreased. Ho: u = 14.7 H1: u < 14.7 (claim) To test this claim, a random sample of 80 completion times under new management was taken. The sample had a mean of 14.2 minutes. --------------------------------- Can we support, at the 0.01 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed. ---------------- The value of the test statistic (round to at least 3 decicmal places)? t(14.2) = (14.2-14.7)/[1.7/sqrt(80)] = -2.6307 --------------------- The p-value(round to at least 3 decimal places)? P-value = P(t< -2.6307 when df = 79) = 0.0051 ------ Conclusion: Since the p-value is less than 1%, reject Ho. The test results support the new management's claim. --------- Cheers, Stan H. ==========

Probability-and-statistics/481284: there are 6 people on the ballot for regional judges. voters can vote for any 4. voters can vote for 0,1,2,2,4 judges. in how many different ways can a person vote thank you for your help 1 solutions Answer 329584 by stanbon(57967)   on 2011-08-13 20:47:17 (Show Source): You can put this solution on YOUR website! there are 6 people on the ballot for regional judges. voters can vote for any 4. voters can vote for 0,1,2,3,4 judges. in how many different ways can a person vote ---- 6C0 + 6C1 + 6C2 + 6C3 + 6C4 ---- = 1 + 6 + 15 + 20 + 15 --- = 57 ============= Cheers, Stan H. =============

Complex_Numbers/481301: Solve the equation in the complex number system: 65x^2 +1 =8x I'm so lost on how to even begin this! 1 solutions Answer 329581 by stanbon(57967)   on 2011-08-13 20:35:33 (Show Source): You can put this solution on YOUR website! Solve the equation in the complex number system: 65x^2 +1 =8x ----- 65x^2-8x+1 = 0 ------- Quadratic Formula: x = [8 +- sqrt(64-4*65*1)]/130 -------- x = [8 +- sqrt(-196)]/130 --- x = [8 +- 14i]/130 --- x = 4/65 +- (7/65)i ======================== Cheers, Stan H. ==============

Miscellaneous_Word_Problems/481148: "A recent study determined that the distance employees at a pharmaceutical company in New Jersey commute to work each way is normally distributed with a mean equal to 13.4 miles and a standard deviation of 3.6 miles. Management has decided to give a year-end bonus to employees who commute large distances and have decided to give the bonus to any employee who commutes over 18.7 miles. Based on this information, approximately 13.3 percent of the employees will get the year-end bonus." Assignment: Consider this situation and respond as to whether you agree with Management's conclusion that 13.3 percent of the employees will get the year-end bonus. Provide your rationale if you disagree with Management and provide the correct percent. 1 solutions Answer 329490 by stanbon(57967)   on 2011-08-13 09:08:49 (Show Source): You can put this solution on YOUR website! A recent study determined that the distance employees at a pharmaceutical company in New Jersey commute to work each way is normally distributed with a mean equal to 13.4 miles and a standard deviation of 3.6 miles. -------------------------- Management has decided to give a year-end bonus to employees who commute large distances and have decided to give the bonus to any employee who commutes over 18.7 miles. Based on this information, approximately 13.3 percent of the employees will get the year-end bonus." --- z(18.7) = (18.7-13.4)/3.6 = 1.5143 --- P(x > 18.7) = P(z > 1.5143) = 0.0650 or 6.5% ================ Cheers, Stan H.

Quadratic_Equations/481141: Let x represent the number of pounds of apples sold at $1.49 per pound, and let y represent the total price paid for the apples. Write an equation for this situation. Then give the ordered pair with an x value of 4 associated with this equation. 1 solutions Answer 329488 by stanbon(57967)   on 2011-08-13 09:03:11 (Show Source): You can put this solution on YOUR website! Let x represent the number of pounds of apples sold at $1.49 per pound, and let y represent the total price paid for the apples. Write an equation for this situation. Then give the ordered pair with an x value of 4 associated with this equation. ------------------- y = 1.49x --- f(4) = 1.49*4 = $5.96 ---------------------- Cheers, Stan H.

Probability-and-statistics/481138: Sam has a bucket of blocks. He has 3 yellow blocks, 10 blue blocks, 6 green blocks, 8 red blocks, and 3 purple blocks. What is the probability he picks a red block? 1 solutions Answer 329486 by stanbon(57967)   on 2011-08-13 08:57:05 (Show Source): You can put this solution on YOUR website! Sam has a bucket of blocks. He has 3 yellow blocks, 10 blue blocks, 6 green blocks, 8 red blocks, and 3 purple blocks. What is the probabilty he picks a red block? ---- P(red) = 8/(30) = 4/15 ----------------------------- Cheers, Stan H. =============

Quadratic_Equations/481146: Don fenced in a rectangular garden in his yard. The length of the rectangle is 5 feet longer than the width and the perimeter is 62 feet. What is the width of the rectangle? 1 solutions Answer 329484 by stanbon(57967)   on 2011-08-13 08:51:10 (Show Source): You can put this solution on YOUR website! Don fenced in a rectangular garden in his yard. The length of the rectangle is 5 feet longer than the width and the perimeter is 62 feet. What is the width of the rectangle? --- Perimeter = 2(L + W) Let width = W Then length = W+5 --- Equation: 62 = 2(W+5 + W) 31 = 2W+5 2W = 26 W = 13 ft. - L = 18 ft. ============= Cheers, Stan H. =============

Quadratic_Equations/481147: The product of two consecutive integers is 4 less than 4 times their sum. Find them 1 solutions Answer 329483 by stanbon(57967)   on 2011-08-13 08:47:27 (Show Source): You can put this solution on YOUR website! The product of two consecutive integers is 4 less than 4 times their sum. 1st: x 2nd: x+1 ----- Equation: x(x+1) = = 4(2x+1)+4 x^2+x = 8x+8 x(x+1) = 8(x+1) x = 8 x+1 = 9 =============== Cheers, Stan H.

Rate-of-work-word-problems/481129: If 15 workers can paint 18 houses in 24 days, how many days will 40 workers take to paint 22 houses? 1 solutions Answer 329475 by stanbon(57967)   on 2011-08-13 07:19:14 (Show Source): You can put this solution on YOUR website! If 15 workers can paint 18 houses in 24 days, how many days will 40 workers take to paint 22 houses? -------------- # of days are inversely related to # of workers and directly related to # of houses. -------------- d = kh/w --- Solve for "k" using "15 workers can paint 18 houses in 24 days" 24 = k*18/15 k = 15*24/18 = 15*(4/3) = 20 -------------- Equation: d = 20h/w --- Solve: How many days will 40 workers take to paint 22 houses? d = 20*22/40 d = 11 days =================== Cheers, Stan H. ===================

Inverses/481128: The one-to-one function is defined by f(x) = x/(8-9x) Find f^-1, the inverse of f . Then, give the domain and range of f^-1 using interval notation. 1 solutions Answer 329473 by stanbon(57967)   on 2011-08-13 07:12:26 (Show Source): You can put this solution on YOUR website! The one-to-one function is defined by f(x) = x/(8-9x) Find f^-1, the inverse of f . ----- 1st: Interchange x and y to get: x = y/(8-9y) 2nd: Solve for "y": 8x-9xy = y --- y+9xy = 8x y(9x+1) = 8x f^-1(x) = 8x/(9x+1) ----- Domain: All Real Numbers except x = -1/9 Range: All Real Numbers except y = 8/9 ========================================= Cheers, Stan H. Then, give the domain and range of f^-1 using interval notation.

Probability-and-statistics/481101: Please help me solve: A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 121 greeting cards indicates a mean value of $3.92 and a standard deviation of $0.45. a. Assuming a normal distribution, construct a 90% confidence interval estimate of the mean value of all greeting cards in the store's inventory. b. Suppose there were 3,000 greeting cards in the inventory. How are the results useful in assisting the owner to estimate the total value of her inventory. 1 solutions Answer 329472 by stanbon(57967)   on 2011-08-13 06:43:11 (Show Source): You can put this solution on YOUR website! A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 121 greeting cards indicates a mean value of $3.92 and a standard deviation of $0.45. a. Assuming a normal distribution, construct a 90% confidence interval estimate of the mean value of all greeting cards in the store's inventory. x-bar = 3.92 ME = 1.645*0.45/sqrt(121) = 0.07 -- 90% CI: 3.92-0.07 < u < 3.92+0.07 ========================================== b. Suppose there were 3,000 greeting cards in the inventory. How are the results useful in assisting the owner to estimate the total value of her inventory. With 90% confidence she can conclude the total value is between 3000*3.85 and 3000*3.99 =========================== Cheers, Stan H. ==========

Probability-and-statistics/481108: A survey of 750 workers were asked how much they use the internet at work. 456 said they used it within limits, and 166 said they did not use the Internet at work. a. Construct a 95% confidence interval estimate for the proportion of all workers who use it within limits. b. Construct the same for those who did not use the internet. 1 solutions Answer 329471 by stanbon(57967)   on 2011-08-13 06:36:54 (Show Source): You can put this solution on YOUR website! A survey of 750 workers were asked how much they use the internet at work. 456 said they used it within limits, and 166 said they did not use the Internet at work. a. Construct a 95% confidence interval estimate for the proportion of all workers who use it within limits. --- p-hat = 456/750 = 0.61 ME = 1.96*sqrt[0.61*0.59/750] = 0.04 -- 95% CI: 0.61-0.04 < p < 0.61+0.04 ===================================== Cheers, Stan H. b. Construct the same for those who did not use the internet. Same procedure.

Probability-and-statistics/481114: Use the Empirical rule to find what two values 95% of the data will fall between for a data set with a mean of 254 and standard deviation of 16. 1 solutions Answer 329470 by stanbon(57967)   on 2011-08-13 06:32:00 (Show Source): You can put this solution on YOUR website! Find the values 2 standard deviations above and 2 standard deviations below the mean. Cheers, Stan H.

Permutations/481076: A club with 27 members is to select five officers:President, Vice President, Secretary,Treasurer, and Historian. In how many ways can this be done? 1 solutions Answer 329444 by stanbon(57967)   on 2011-08-12 23:50:32 (Show Source): You can put this solution on YOUR website! A club with 27 members is to select five officers:President, Vice President, Secretary,Treasurer, and Historian. In how many ways can this be done? ---- Ans: 27P5 = 27!/(27-5)! = 27!/22! = 27*26*25*24*23 = 9687600 ============ Cheers, Stan H.

Permutations/481077: there are 20 people in the room and i need to make a committee of 6 of them. each member is equal. in how many ways can this be done? 1 solutions Answer 329443 by stanbon(57967)   on 2011-08-12 23:47:12 (Show Source): You can put this solution on YOUR website! there are 20 people in the room and i need to make a committee of 6 of them. each member is equal. in how many ways can this be done? --- Ans: 20C6 = 20!/[14!*6!] = (20*19*18*17*16*15)/(1*2*3*4*5*6) = 38760 ============= Cheers, Stan H.

Probability-and-statistics/481093: Person A and Person B are doing target practice. Person A hits the target with a probability of 0.8, while Person B hits the target with a probability of 0.9. What is the probability that Person B hit the target given that both of them fired and exactly one shot hit the target? a. 0.18 b. 0.30 c. 0.69 d. 0.90 I came up with .50*.80 =.40 and .50*.90=.45 thus .40*.45=0.18 Is this correct? Thank you 1 solutions Answer 329442 by stanbon(57967)   on 2011-08-12 23:43:40 (Show Source): You can put this solution on YOUR website! Person A and Person B are doing target practice. Person A hits the target with a probability of 0.8, while Person B hits the target with a probability of 0.9. What is the probability that Person B hit the target given that both of them fired and exactly one shot hit the target? --- The events are independent. --- P(B hit and A missed) = 0.9*0.2 = 0.18 --- Cheers, Stan H. a. 0.18 b. 0.30 c. 0.69 d. 0.90

Probability-and-statistics/481091: The probability that event A will occur is 40%, while the probability that event B will occur is 60%. What is the probability that event A or event B will occur, if the events are indendent? a. 20% b. 24% c. 76% d. 100% Thank you . 1 solutions Answer 329441 by stanbon(57967)   on 2011-08-12 23:16:23 (Show Source): You can put this solution on YOUR website! The probability that event A will occur is 40%, while the probability that event B will occur is 60%. What is the probability that event A or event B will occur, if the events are indendent? --- If the events are independent P(A and B) = P(A)*P(B) = 0.4*0.6 = 0.24 =============== Cheers, Stan H. ============= a. 20% b. 24% c. 76% d. 100%

Polynomials-and-rational-expressions/481098: Pls help me to solve this Euation : 2x^3-22x^2+120x-45=0,Find value of x 1 solutions Answer 329440 by stanbon(57967)   on 2011-08-12 23:13:15 (Show Source): You can put this solution on YOUR website! 2x^3-22x^2+120x-45=0,Find value of x ---- I graphed it. There is a Real zero around x = 0.4038.. The other zeroes are complex numbers. ============ Cheers, Stan H.

Rectangles/481097: the perimeter of a rectangular photograph is 36cm . the length is 4 cm greater than the width. find the width and the length 1 solutions Answer 329439 by stanbon(57967)   on 2011-08-12 23:06:17 (Show Source): You can put this solution on YOUR website! the perimeter of a rectangular photograph is 36cm . the length is 4 cm greater than the width. find the width and the length ---- Perimeter = 2(length + width) P = 2(L+W) -------- 36 = 2(W + (W+4)) --- 18 = 2W + 4 2W = 14 Width = 7 cm --- Length = W + 4 = 11 cm ====================== Cheers, Stan H. ================

test/481096: Please help me the problem# 31 reads so in my text book. In a circle,the diameter is twice the langth of the radius r. Can someone please help me solve this and understand it. Thank you very much. 1 solutions Answer 329437 by stanbon(57967)   on 2011-08-12 23:03:42 (Show Source): You can put this solution on YOUR website! Please help me the problem# 31 reads so in my text book. In a circle,the diameter is twice the langth of the radius r. Can someone please help me solve this and understand it. Thank you very much. --- That is not the statement of a problem. It is a statement of a fact. The diameter of a circle is always twice the length of the radius of that circle. ---------------- Cheers, Stan H.

Polynomials-and-rational-expressions/481092: Please help with one last question.. x^2+5x-43/x+9 Thanks, 1 solutions Answer 329436 by stanbon(57967)   on 2011-08-12 22:58:16 (Show Source): You can put this solution on YOUR website! x^2+5x-43/x+9 --- Using synthetic division: -9)....1....5....-43 ........1....-4...|..-7 Quotient: x + 4 Remainder: -7 =================== Cheers, Stan H. ===================

Probability-and-statistics/481082: In a recent study 90 percent of the homes in the United States were found to have color TVs. In a sample of nine homes, what is the probability that: a. All nine have color TVs? b. Less than five have color TVs? c. More than five have color TVs? d. At least seven homes have color TVs? I am confused I was told this problem is Binomial but I can't seem to solve it can someone please help me out please. Thank you very much. 1 solutions Answer 329426 by stanbon(57967)   on 2011-08-12 22:19:45 (Show Source): You can put this solution on YOUR website! In a recent study 90 percent of the homes in the United States were found to have color TVs. In a sample of nine homes, what is the probability that: ---- Binomial Problem with n = 9 and p = 0.9 ---- a. All nine have color TVs? P(x=9) = 9C9(0.9)^9*(0.1)^0 = 0.9^9 = 0.3874 ---------------------------------------------------- b. Less than five have color TVs? P(0<= x <=4) = binomcdf(9,0.9,4) = 0.0008909 ----------------------------------------- c. More than five have color TVs? P(6<= x <=9) = 1 - binomcdf(9,0.9,5) = 0.9917 ----------------------------------------- d. At least seven homes have color TVs? P(7<= x <=9) = 1-binomcdf(9,0.9,6) = 0.9470 ================================== I used a TI-84 to get the cumulative probabilities. Cheers, Stan H.

Probability-and-statistics/481060: A certain population has a mean of 500 and a standard deviation of 30. Many samples of size 36 are randomly selected and the means are calculated. What value would you expect to find for the mean of all these samples means? (round to the nearest integer) What value would you expect to find for the standard deviation of all these sample means? (round to the nearest integer) True of False, you would expect the shape of the sampling distribution to be approximately normal 1 solutions Answer 329424 by stanbon(57967)   on 2011-08-12 22:01:29 (Show Source): You can put this solution on YOUR website! A certain population has a mean of 500 and a standard deviation of 30. Many samples of size 36 are randomly selected and the means are calculated. What value would you expect to find for the mean of all these samples means? Ans: The mean of the sample means = the mean of the population Ans: 500 --------------------------- What value would you expect to find for the standard deviation of all these sample means? Ans: 30/sqrt(36) = 30/6 = 5 ----------------------------------- True of False, you would expect the shape of the sampling distribution to be approximately normal True. --- All of these answers are provided by the Central Limit Theorem. Cheers, Stan H.