# Questions on Algebra: Probability and statistics answered by real tutors!

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 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Question 459097: Write the claim mathematically, identify Ho and Ha, find critical values and rejection regions. Use them to answer the question. A light bulb manufacture guarantees that the mean life of bulbs is at least 750 hours with a standard deviation of 60 hours. At alpha = 0.02, do you have enough evidence to reject his claim? Click here to see answer by jim_thompson5910(29613)

 Question 459172: Selecting 3 cards (without replacement) from a regular deck of 52 cards (assume order is not important) Picking 2 letters from the alphabets ( no repetitions allowed; assume order is important) Click here to see answer by robertb(4012)

 Question 459221: a bag contains 3 red discs, 4 black discs and 5 yellow discs. 2 discs are picked one after the other without replacement. Find the probability that a) the first disc is black and the second is red b) the first and second discs are yellow c) the first is red and e second is yellow Click here to see answer by stanbon(60778)

 Question 459224: Seven runners are racing against each other in a track meet. In how many ways can these runners be in first, second, and third place (assume there cannot be any ties). Click here to see answer by stanbon(60778)

 Question 459202: Show all work. Mary purchased a package of 15 different plants, but she only needed 10 plants for planting. In how many ways can she select the 10 plants from the package to be planted? Click here to see answer by sudhanshu_kmr(1152)

 Question 459356: 4. A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting •a prime number under 10 given the card is red. (1 is not prime.) •a King, given that the card is not a heart. •a nine given the card is a face card. Show step by step work. Give all solutions exactly in reduced fraction form. Click here to see answer by Edwin McCravy(9719)

 Question 459388: What is the value of C (7, 2)? Click here to see answer by sudhanshu_kmr(1152)

 Question 459351: . A particular hair treatment program has caused hair growth in 70% of its users. A random sample of 20 users is obtained. Using the Binomial Probability Distribution, determine the following probabilities: a) That exactly 15 experienced hair growth. b) That less than 9 experienced hair growth. c) That more than 12 experience hair growth. d) That 15 or more experience hair growth. Click here to see answer by edjones(7794)

 Question 459491: In a science class there are 12 boys and 10 girls. What is the probabilty that a lab group of 5 people is created consisting of exactly 4 boys and 1 girl? Click here to see answer by edjones(7794)

 Question 459474: A light bulb manufacture guarantees that the mean life of bulbs is at least 750 hours. A random sample of 36 bulbs has a mean life of 745 with a standard deviation of 60 hours. At alpha = 0.02, do you have enough evidence to reject his claim? Click here to see answer by edjones(7794)

 Question 459280: Eighty percent of married couples paid for their honeymoon themselves. You randomly select 20 married couples and ask if they paid for their honeymoon themselves. Find the probability that the number of couples who say they paid for their honeymoon themselves is: a) exactly fifteen b) at least twelve c) less than twelve Click here to see answer by math-vortex(472)

 Question 459596: in class of thirty students , seven have blue eyes what is the probability that a person does not have blue eyes Click here to see answer by sudhanshu_kmr(1152)

 Question 459651: There are 6 students who all want to be in group of 3 people chosen to speak at graduation. How many different groups can be chosen? Click here to see answer by sudhanshu_kmr(1152)

 Question 459584: Assume that the population of heights of female college students is approximately normally distributed with mean m of 67.16 inches and standard deviation s of 4.82 inches. A random sample of 92 heights is obtained. Show all work. (A) Find the mean and standard error of the x distribution (B) Find P(x > 67.75) Click here to see answer by stanbon(60778)

 Question 459688: HOW MANY DIFFERENT SETS OF THREE CAN I MAKE OUT OF 75 DIFFERENT NUMBERS? NO TWO SET CONTAIN THE SAME 3 NUMBERS. Click here to see answer by sudhanshu_kmr(1152)

 Question 459740: In a pack of 52 cards, there are 13 of each suit. What is the probability of reaching into a deck and pulling out a heart? Click here to see answer by Alan3354(34679)

 Question 459844: A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 95% confident that her estimate is correct. If the standard deviation is 4.02, how large a sample is needed to get the desired information to be accurate within 0.58 decibels? Show all work. Click here to see answer by stanbon(60778)

 Question 459853: Should I sacrifice near-normality in order to run regression analysis in Excel2007? The first part of my assignment was correcting for missing data. Seeing that some of the variables were anything but normal, I removed outliers. This left me with uneven sample sizes. If I am trying to analyze the factors affecting hospital cost don't I have to run regression analysis? When I try to do it in excel it obviously won't allow me to do it since the sample sizes are not equivalent. So, if I am interested in how the different factors affect cost, do I remove the outliers in cost variable (y), and subsequently remove the accompanying variables across the board? List wise deletion except to correct for outliers? Or do I just accept that the majority of these are skewed and go from there? Any guidance would be appreciated. My Ocd tendencies are not good when taking an introductory biostats class LOL. Thanks in advance! Here are my desc stats w/ orig data Mean 125636198.1 85 137 967 3100 18507 20577 2082 651 Median 77698890.47 48 134 498 1251 8582 20833 1296 420 Mode #N/A 15 124 4771 #N/A #N/A 0 #N/A 0 Standard Deviation 163253552.2 102 30 1178 4491 25771 16569 2244 792 Sample Variance 2.66517E+16 10468.92 887.90 1386601.94 20169352.31 664147515.61 274531737.27 5034278.69 626619.76 Kurtosis 19.36996943 7.47 -0.19 4.45 4.97 7.61 1.77 4.61 3.88 Skewness 3.862249824 2.48 0.41 2.24 2.31 2.65 1.08 2.07 2.00 Range 1118414097 537 128 4842 21092 133432 83229 10913 3669 Minimum 11017817.58 2 78 1 49 435 0 98 0 Maximum 1129431915 539 206 4843 21141 133867 83229 11011 3669 Sum 9673987257 6497 10112 73467 229400 1425053 1605018 154057 50098 Count 77 76 74 76 74 77 78 74 77 Below shows descriptive statistics afterthe removal of outliers & missing data Mean 71.79631515 59 133 581 1226 9711 16776 1392 384 Median 66.9061 40 133 431 938 7502.5 16856 1204.5 381 Mode #N/A 40 124 431 #N/A #N/A 0 #N/A 0 Standard Deviation 41.44398741 53 25 453 1016 8129 10960 1135 349 Sample Variance 1717.604093 2859 650 204778 1031616 66077065 120111788 1287801 121824 Kurtosis 0.491434794 0.268559434 0.088756826 0.80076461 2.047540427 0.26399267 -0.992319081 1.308159612 0.93664116 Skewness 0.859322829 1.040215988 0.304137886 1.117717591 1.372018541 1.069535728 -0.069213819 1.286450345 0.974957725 Range 183.414746 222 108 1970 4765 31075 37873 4599 1502 Minimum 11.017818 2 83 8 49 723 0 98 0 Maximum 194.432564 224 191 1978 4814 31798 37873 4697 1502 Sum 3805.204703 3375 7599 31964 62532 524388 956256 75158 21123 Count 53 57 57 55 51 54 57 54 55 Confidence Level(95.0%) 11.42337744 14.18755301 6.765346749 122.3344783 285.6660103 2218.729794 2907.960637 309.7443555 94.35664243 Original Data (No Adjustments) Mean 125636198.1 85 137 967 3100 18507 20577 2082 651 Median 77698890.47 48 134 498 1251 8582 20833 1296 420 Mode #N/A 15 124 4771 #N/A #N/A 0 #N/A 0 Standard Deviation 163253552.2 102 30 1178 4491 25771 16569 2244 792 Sample Variance 2.66517E+16 10468.92 887.90 1386601.94 20169352.31 664147515.61 274531737.27 5034278.69 626619.76 Kurtosis 19.36996943 7.47 -0.19 4.45 4.97 7.61 1.77 4.61 3.88 Skewness 3.862249824 2.48 0.41 2.24 2.31 2.65 1.08 2.07 2.00 Range 1118414097 537 128 4842 21092 133432 83229 10913 3669 Minimum 11017817.58 2 78 1 49 435 0 98 0 Maximum 1129431915 539 206 4843 21141 133867 83229 11011 3669 Sum 9673987257 6497 10112 73467 229400 1425053 1605018 154057 50098 Count 77 76 74 76 74 77 78 74 77 orig. data set Hospital Total Beds in the Hospital Total Number of Services offered in the facility Total operating cost per year Full-Time Equivalents Case Mix Adjusted Discharges Total Surgical Visits per year Total ER Visits per year Total Ambulatory Visits per year Total Live Births per year 1 60 140 64331896 376 1282 6898 24126 1393 702 2 65 140 122146708 582 2277 7075 11402 251 250 3 43 144 46481090 303 661 2970 9753 1287 443 4 122 152 135096200 857 3311 21494 25580 3289 1502 5 79 170 233734561 1395 5756 32258 59382 3076 6 60 149 159399584 734 12978 35053 2621 750 7 78 110 1129431915 572 1468 24319 27641 2911 8 40 124 101344345 496 1220 6402 16856 853 416 9 77 135 107606586 456 1098 8566 33607 1115 462 10 20 136 52811772 503 1579 8582 22893 1544 714 11 121 71332538 476 921 8905 22497 568 129 12 75 149 80100410 886 1645 11186 30815 1483 238 13 40 136 47997004 71 231 6574 0 625 0 14 114 149 106953900 1050 2800 17868 31857 1861 789 15 29 135 66159737 181 406 7530 0 928 0 16 60 128 77698890 374 919 6004 0 749 0 17 86 149 72571020 490 2294 11024 26801 1305 702 18 20 33890360 318 541 435 1874 453 353 19 92 144 90378372 1080 2000 11954 37873 1700 1200 20 40 133 72571812 130 1366 5656 14841 997 449 21 224 198 354097261 2686 12966 71663 30207 8792 0 22 134 197 252896395 1302 7041 22066 35080 5400 0 23 150 187 99809865 1213 4814 26267 23052 3146 1067 24 140 189 291002040 4771 10530 66084 51377 6193 1750 25 210 206 2713 12000 42050 41104 5109 2682 26 250 195 635719011 4609 16636 76728 19670 11011 0 27 150 157 159291211 1418 6437 31798 34890 3908 660 28 155 191 240386978 1694 7856 54653 52290 4695 2956 29 2 83 47824729 8 122 7699 0 325 0 30 2 86 39505252 192 583 7427 0 363 114 31 131 136 168112580 1368 41119 51141 4277 1076 32 30 106 50374425 361 614 1775 12525 869 0 33 101 133 101811566 962 1739 11042 22105 1807 720 34 180 132674596 1374 3504 19576 38521 3165 1619 35 150 145 133246519 1512 3283 23641 26454 3421 1616 36 2 78 42533051 1 170 7602 0 0 37 23 147 42267738 431 643 2375 22863 307 435 38 131 121 110985783 934 938 15479 24475 1723 0 39 106 131 57585450 755 1212 8265 12114 1211 381 40 11 112 20608644 125 155 1230 1624 98 26 41 13 87 11017818 165 175 723 0 177 88 42 29 121 41110232 328 3568 0 1195 301 43 26 124 32987171 311 600 3795 5122 453 199 44 25 102 29925571 328 963 3518 20964 918 418 45 104 133 127582023 1126 2517 27604 5213 604 46 50 132 32715235 22 416 3487 8201 340 183 47 124 31993465 324 508 2954 4556 457 141 48 17 106 24856133 375 285 1997 6104 289 144 49 39 109 35320048 408 794 1306 15178 400 474 50 412 155 268521593 3991 10668 76140 20702 9672 2089 51 203 80725005 3296 13570 21178 2395 1028 52 477 180 449112700 4771 16467 133867 83229 6918 3669 53 539 184 457043818 4843 21141 119776 55583 2673 54 166 115 72454403 499 922 8876 18711 1423 533 55 15 137 87091348 195 972 15498 21008 2355 0 56 30 135 81495413 431 1198 6815 23313 1198 1092 57 6 94 21660247 222 204 2463 0 389 273 58 6 100 24620386 241 281 2008 0 413 222 59 10 107 23872832 229 491 2667 1117 455 253 60 7 106 28000000 330 375 1800 13370 512 270 61 15 120 37778177 415 455 2510 7333 536 266 62 15 154 96849621 190 1521 11434 10001 2092 0 63 2 101 15783121 90 49 792 5190 187 0 64 100 145 78819659 459 1803 7475 14531 1261 481 65 20 130 43505204 622 907 1183 15825 1257 518 66 3 92 18907920 157 1572 7567 420 0 67 15 122 29631482 321 2139 5676 500 255 68 20 122 70935956 725 1358 16250 15760 1387 493 69 15 124 58431299 158 165 2586 11762 344 420 70 9 123 66906100 198 500 10000 14500 1000 0 71 45 170 194432564 1038 3163 25517 21722 2323 432 72 110 186 165151572 1978 6668 26977 32893 4697 742 73 25 124 51467691 697 933 7918 22939 1560 273 74 52 155 143039315 1198 2749 26983 28938 2960 702 75 40 143 87885000 963 2401 18123 26512 2321 850 76 25 131 80641895 735 1660 12840 23097 2658 527 77 245 177 435805108 3888 15682 75068 52645 1801 78 85 183138339 1066 3768 13643 9846 1634 407 Click here to see answer by math-vortex(472)

 Question 459888: Nine software engineers were interviewed to develop an estimate for software lines of code. The mean estimate is 12480 lines of code with a standard deviation of 2400 lines of code. Develop an 80% confidence interval for the population mean. (Carry intermediate calculations to three decimal places.) 11362 ≤ µ ≤ 13598 12107 ≤ µ ≤ 12853 11769 ≤ µ ≤ 13191 11374 ≤ µ ≤ 13586 Click here to see answer by jim_thompson5910(29613)

 Question 459797: plzzz helppp !!!! A surgeon makes a medical operation successfully with a probability p=0,8. he will make n=10 medçal operations for a week. what is the probabity of the following evetns: 1) A={ the number of succesful operations is 6} 2)B={at least one of the 10 operations is succesfull} 3)C={the number of succesfu operations is less then 10} 4) find the most probable number of N of the succesfull operations, made by this surgeon. Click here to see answer by sudhanshu_kmr(1152)

 Question 460024: If the class average is 195 and the SD is 30, what would be the score 1 SD above and below the mean? Click here to see answer by jim_thompson5910(29613)

 Question 460068: There are 10 light bulbs in a bag. Two are defective. Select a light bulb. What is the probablity of selecting a light bulb the is not defective.? Click here to see answer by stanbon(60778)

 Question 460099: how many ways can a person select television commercials from 11 television commercials? Click here to see answer by Alan3354(34679)
 Question 460099: how many ways can a person select television commercials from 11 television commercials? Click here to see answer by richard1234(5390)

 Question 460104: how many ways can a person select 7 television commercials from 11 television commercials? Click here to see answer by Alan3354(34679)

 Question 460023: A bag contains 7 lavender marbles, 11 turquoise marbles and 5 rainbow marbles. What is the chance of drawing a rainbow marble? If a rainbow marble is drawn then placed back into the bag, and a second marble is drawn, what is the probability of drawing a lavender marble? Give solutions exactly in reduced fraction form, separated by a comma. Click here to see answer by Alan3354(34679)

 Question 460125: Q:1- A bag contains 4 white and 3 black balls and two balls are drawn at random. Find the probability that (i)Both are white (ii)Both are black (iii)one white and one black. Q:2- From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability that it is a (i)King (ii)Card of spades (iii)red card (iv)black card (v)a picture card (vi)an ace (vii)jack of clubs. Q:3- A coin is tossed twice. Find the probability that at least one head turns up. Click here to see answer by edjones(7794)

 Question 460098: a jazz band has prepared 18 selections for a concert tour. At each stop they will perform 10. Hoa many different programs are possible? How many programs are possible if they always begin with the same song and end with the same song? Click here to see answer by stanbon(60778)

 Question 460077: how many ways can 8 instructors be assigned to 7 courses in mathmatics Click here to see answer by stanbon(60778)
 Question 460077: how many ways can 8 instructors be assigned to 7 courses in mathmatics Click here to see answer by navya4u2004(1)
 Question 460077: how many ways can 8 instructors be assigned to 7 courses in mathmatics Click here to see answer by Alan3354(34679)

 Question 460170: there are 10 bicyclist entered in a race. in how many different orders could these 10 bicylist finish? Click here to see answer by Alan3354(34679)

 Question 460207: its a word problem .. if out of a deck i use 20 cards ... 5 suits and 4 of each card.. what is the propability that i will chose 4 cards in the exact order as 4 random generated cards and is the propability greater than if i use 5 cards of 4 suits ? is it less than or is it equal to also this is to neither homework or test . i am trying to make a board game Click here to see answer by Edwin McCravy(9719)

 Question 460238: 2tail test with rejecting region Alfa_.050, n=16 d.f.15, sample mean .950, standar deviation =.01 Ho' m=1 Hi m =/ 1 Click here to see answer by stanbon(60778)

 Question 460258: each of the numbers 0-9 is written on a piece of paper and all of the pieces of paper are placed in a hot. one number is selected. determine the probability that the number is even.(0 is an even #) is it 1/10, 1/9,2/5 or 1/2? Click here to see answer by checkley79(3056)

 Question 460314: Two dice are rolled, find the probability that the sum is odd and the number on one of the dice is a 3. Click here to see answer by edjones(7794)

 Question 460322: consider the venn diagram below. Determine: n(A) n(B) p(A) p(B) p(A|B) p(B|A) Thanks very much for your help! Click here to see answer by Edwin McCravy(9719)

 Question 460351: If 50 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win 2 prizes if that person buys 2 tickets Click here to see answer by stanbon(60778)

 Question 460374: An identification code is to consist of four letters followed by three digits. How many different codes are possible if repetition is permitted? Click here to see answer by stanbon(60778)

 Question 460391: Sixty-eight students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .05, is the degree of certainty independent of credits earned? Certainty Certainty of Major by Credits Earned Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total 0 - 9 12 8 3 23 10-59 10 7 8 25 60 or more 5 9 10 24 Col Total 27 24 21 72 I calculated this..is it look correct? I'm not sure how to write a conclusion Chi-square Contingency Table Test for Independence Col 1 Col 2 Col 3 Total Row 1 12 8 3 23 Row 2 8 4 10 22 Row 3 1 7 11 19 Total 21 19 24 64 14.76 chi-square 4 df .0052 p-value Ho: column and row factors are independent Ha: these are dependent Test statistic: chi-square = 14.76 P – value : .0052 Df = (5-1)(5-1) = 4 Click here to see answer by stanbon(60778)

 Question 460395: Help me,,, Given ∫_A▒〖[1/π(1+x^2 ) ] dx〗, where A ⊂ "A" = {x : -∞ < x < ∞}. Show that the integral could serve as a probability set function of a random variable X whose space is "A" . Let the probability set function of the random variable X be P(A) = ∫_A▒〖e^(-x) dx,〗 where "A" = {x : 0 < x < ∞}. Let Ak = {x : 2 – 1/k < x ≤3}, k = 1, 2, 3,….. Find lim┬(k→∞)⁡〖A_k 〗 and P(lim┬(k→∞)⁡〖A_k 〗). Find P(Ak) and 〖lim┬(k→∞) P(〗⁡〖A_k 〗). Note that 〖lim┬(k→∞) P(〗⁡〖A_k 〗) = P(lim┬(k→∞)⁡〖A_k 〗). Click here to see answer by robertb(4012)

 Question 460382: Cable Television In 2006, 86%of U.S. households had cable TV. Choose 3 households at random.find the probability that a. None of the 3 households had cable TV b. All 3 households had cable Tv Click here to see answer by robertb(4012)

 Question 460427: If a hospital delivers 8 babies in one hour, what is the probability that it will deliver 7 babies in the next hour? Click here to see answer by richwmiller(10283)