Positive Relationship between Financial Decisions and Values of Firms - Essay Example

? Finance and Accounting Introduction Basing on the principle of the central limit theorem, a sampling distribution of statistics becomes normal or near to being normal whenever the sampling size is large enough. When applying this principle for a sampling distribution of the mean, it is possible to find the sample distribution of the means by supposing that if one draws all possible samples of say size n from a given population of say size N, and supposes the mean score for the samples is computed separately, then the sample distribution of the means can be obtained. In this case, the population mean (?) is often equal to the sampling distribution mean, and the standard error of such sampling distribution (?x) can be determined using the population standard deviation (?), the sample size and the population size. Using mathematical equation, the equations below serve to indicate the mathematical relation between the population mean and the sampling distribution, and the relation between the sample distribution, the population standard deviation, the populationa dn the sample size as shown ?x = ? and ?x = ? * sqrt(1/n - 1/N ) Basing on the mathematical expressions above, it is possible to specify the sampling distribution of the mean unless two conditions are met. First, when the population is said to be normally distributed or otherwise if the sample size is said to be sufficiently large. Secondly, the standard population of the population is known. In this problem, the two conditions are met and, therefore, given the standard deviations, and the means of the five samples given, the mean of the population can be calculated through averaging the sample means. This can be accomplished mathematically, as the population mean = (80934 + 78110.48 + 80,340 + 84716.5)/5 = 64,890.196 $. In a sampling distribution of means, the populations mean (?) has been found to always equal to the sampling distribution (?x) mean. Clearly, the sample distribution is equal to 64,890.196 $. In order to find the standard error of a sampling distribution, the important parameters are the population’s standard deviation, the size of the sample, as well as the population size. In this case, the standard deviation of the population is found by averaging the standard deviation as (809.34 + 3888.243 + 3334.5 + 3351.6 + 3332.45)/5 = 2943.22$. From the initial knowledge the standard error of the distribution becomes ?x = ? = 64,890.196$. It is also possible to use the relation ?x = ? * sqrt( 1/n - 1/N to find the standard error of the sampling distribution becomes, which is given by 2943.22 x 0.00137 = 4.03733. Given that the sampling distribution of the mean has been shown to be normally distributed, with a mean of 64,890.196, and the standard error of 4. 03733, in order find the probability that this revenue shall exceed $ 2,2200,000, we shall make use of an online normal distribution calculator. Fitting the these values into a distribution calculator, probability is found to be 0.05. For case II The probability that the revenue shall exceed $, 2,500,000, is found by fitting the values of the standard deviation, the mean and the value $ 2,500,000 into an online normal distribution calculator, which shows that P ( Read More