Statistics for Business Essays

Statistics for Business Essays Statistics for Business Essay Statistics for Business Essay Does asymptotic mean that the normal curve gets closer and closer to the X-axis but never actually touches it? Yes, asymptotic means that the curve of a line will approach 0 (the x-axis), but it will not touch 0 and instead will extend to infinity. In this class, this applies to the normal continuous distribution and is one of the 4 key characteristics of a normal continuous distribution that our text book discusses. This means that the curve of the line will extend infinitely in both the negative and positive direction in exact mirror image patterns on either side of the mean. For a normal probability distribution, is about 95 percent of the area under normal curve within plus and minus two standard deviations of the mean and practically all (99. 73 percent) of the area under the normal curve is within three standard deviations of the mean? Yes. According to the Empirical Rule: -68% of the area under the curve is within +/- 1 standard deviation of the mean -95% of the area under the curve is within +/- 2 standard deviations of the mean -Virtually all, 99. % of the area under the curve is within +/- 3 standard deviations of the mean Is a z-score the distance between a selected value (X) and the population mean (u) divided by the population standard deviation(s)? Yes. We use z-scores to change normal probability distributions into standard normal probability distributions, which are unique because they have a mean of 0 and standard deviation of 1. To convert to a standard normal probability distribution we must find the z-scores for each observation. These are found by subtracting the mean value from the selected value and dividing by the standard deviation. The Normal Probability Distribution Find an example of application of probability theory in your workplace or business. Show that the reasons that your workplace uses probability analysis, such as probability of risk calculations or percent defects or percent for pass or fail of a product, etc. In my company, I do groundwater sampling for remediation projects. When we are finished, we send our samples to a laboratory via FedEx or UPS. The laboratory reports that approximately 2 bottles are broken in every cooler shipped, regardless of how well they are packed. To perform sample analysis, the laboratory needs 1-500 ml bottle of groundwater, and 1-50ml vial of water to perform all of the tests for each well. When we take samples we collect 3-500ml bottles and 3-50 ml vials of groundwater per well because we know that on average two bottles will break per shipment. The bottles that break could be from 2 different wells, or 2 different sized bottles, or they could be two identical sized bottles from the same well. By collecting extra samples, we ensure that we are sending the lab enough samples to accurately perform analysis, and we are ensuring that we don’t have to go back into the field and spend thousands of extra dollars to re-collect samples. What are some of characteristics of a Normal Probability Distribution? According to our text (pg 223), all normal probability distributions have these characteristics: 1. The are bell-shaped and the mean, median, and mode are equal and located in the centre of the distribution. 2. The total area under the curve = 1. 00 with ? f this located to the right of the peak(mean) and ? located to the left of the peak (mean). 3. The distribution curve is symmetrical around the peak (mean) and therefore there are two identical halves of the curve, centred around the mean. 4. The curve approaches the x-axis, but never actually touches it. (i. e. , it is asymptotic) 5. The location is determined by the mean and the dispersion is determined by the standard deviation. Non-stop Airlines determined that the mean number of passengers per flight is 152 with a standard deviation of ten passengers. Practically do all flights have between 142 and 162 passengers? According to the Empirical rule, 142 -162 passengers would fall within 1 standard deviation of the mean (i. e. , 68% of the area under the curve) If we wanted to know how many passengers were on practically/virtually all flights, we would have to apply the Empirical Rule for 3 standard deviations from the mean. This would account for 99. 7% of the area under the curve. According to this theory, virtually all flights would have between 122 – 182 passengers. Is the total area within any continuous probability distribution equal to 1. 00? Yes. If we are a talking about uniform probability distributions (rectangles), the area must equal 1. We can find this using Area = basexheight or (b-a/1) x (1/b-a). Using this equation, both fractions will ‘cancel out’ to give you a value of 1. 00. If we are talking about normal probability distributions, they are bell-shaped with a single peak at the distribution centre and therefore, they are symmetrical about the mean. This means that the two halves of the curve are identical and they both have values of 0. 5 (0. 5 to the left of the mean and 0. 5 to the right of the mean). Is the uniform probability distributions standard deviation proportional to the distributions range? Yes. The equation for standard deviation for a uniform probability distribution is = SQRT [ (b-a)^2/12]. A range is the difference between the max and min values for a distribution (b-a). Therefore, the range of the distribution directly impacts the standard deviation as it is a part of the equation. The larger the range, the larger the standard deviation of a uniform distribution and the smaller the range, the smaller the standard deviation of a uniform distribution. About what percent of the area under the normal curve is within one standard deviation of the mean? According to the Empirical Rule, approximately 68% of the area under the curve, for a normal distribution, is within +/- one standard deviation of the mean. (u +/- 1sd)

Learn About Homonyms and See Examples

Learn About Homonyms and See Examples Homonyms are two or more words that have the same sound or spelling but differ in meaning. Adjectives: homonymic and homonymous. Generally, the term homonym refers both to homophones (words that are pronounced the same but have different meanings, such as pair and pear) and to homographs (words that are spelled the same but have different meanings, such as bow your head and tied in a bow). Note that some dictionaries and textbooks define and distinguish these three terms in different ways. Some equate homonyms only with homophones (words that sound the same). Others equate homonymns only with homographs (words that look the same). See the observations below by Tom McArthur and David Rothwell. Also see Homophones and Homographs: An American Dictionary, 4th ed., by James B. Hobbs (McFarland Company, 2006). Pronunciation HOM-i-nims Etymology From the Greek, same name Examples and Observations Mine is a long and sad tale! said the Mouse, turning to Alice, and sighing.It is a long tail, certainly, said Alice, looking down with wonder at the Mouses tail; but why do you call it sad?(Lewis Carroll, Alices Adventures in Wonderland)Your children need your presence more than your presents.(Jesse Jackson)I enjoy bass fishing and playing the bass guitar.The groups lead singer carried a lead pipe for protection.His death, which happend in his berth,At forty-odd befell:They went and told the sexton, andThe sexton tolld the bell.(Thomas Hood, Faithless Sally Brown)Attend your Church, the parson cries:To church each fair one goes;The old go there to close their eyes,The young to eye their clothes.Mae Maebe Funke: Do you guys know where I could get one of those gold T-shaped pendants?Michael: Thats a cross.Mae Maebe Funke: Across from where?(Alia Shawkat and Jason Bateman in Arrested Development) Homonymy A case of homonymy is one of an ambiguous word whose different senses are far apart from each other and not obviously related to each other in any way with respect to a native speakers intuition. Cases of homonymy seem very definitely to be matters of mere accident or coincidence. (James R. Hurford, Brendan Heasley, and Michael B. Smith, Semantics: A Coursebook, 2nd ed. Cambridge University Press, 2007) Three Kinds of Homonyms There are three kinds [of homonyms]: those that sound and look alike (bank a slope, bank a place for money, and bank a bench or row of switches); homophones, that sound alike but do not look alike (coarse, course); and homographs, that look alike but do not sound alike (the verb lead, the metal lead). . . . There are over 3,000 homographs in the Concise Oxford Dictionary (8th edition, 1990). (Tom McArthur, Oxford Companion to the English Language. Oxford University Press, 1992) Homographs and Homophones The reason that there is confusion and a lack of clarity over homonym is that it is closely related to two other words, homograph and homophone. I shall, therefore, define these words first. It is possible for a word to be a homograph or a homophone. However, whatever the word may be, it is also, by definition, a homonym. In other words, homonym is a conceptual word that embraces both homographs and homophones. . . . [H]omonym is just the collective noun for homograph and homophone. (David Rothwell, Dictionary of Homonyms. Wordsworth, 2007) A homograph is a word that is spelled identically to another word but none the less has a different meaning and probably a different origin. You will doubtless be annoyed if you tear your trousers while climbing over a fence. Indeed, you may be so upset that you shed a tear. As you can see, tear and tear are spelled identically, but they are pronounced differently and have entirely different meanings. They are good examples of a homograph. Many homographs are not even pronounced differently. Thus the word hide sounds exactly the same whether you are talking about the skin of an animal, a measure of land or the verb meaning to conceal or keep out of sight. A homophone is a word that sounds exactly like another word  but has a different meaning and a different spelling. If you stand on the stair and stare at the picture, you have a good example of a couple of homophones. . . . The Lighter Side of Homonyms Secret-keeping is a complicated endeavor. One has to be concerned not only about what one says, but about facial expressions, autonomic reflexes. When I try to deceive, I myself have more nervous tics than a Lyme disease research facility. [pause] Its a joke. It relies on the homonymic relationship between tick, the blood-sucking arachnid, and tic, the involuntary muscular contraction. I made it up myself. (Jim Parsons as Sheldon Cooper in The Bad Fish Paradigm. The Big Bang Theory, 2008) Test your knowledge by taking this  Commonly Confused Words Quiz