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The Normal Distribution and Probability - Essay Example

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Assignment 1 Central tendency is a representative statistics in a population. Whereas mean refers to the average of scores, mode provides the most frequent score while the median is indicates a score that which is in the middle of a distribution. A report of annual incomes from regions in the country is a typical example of a central tendency…
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The Normal Distribution and Probability
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Download file to see previous pages Given that the median helps to do away with influences associated with too much of one or two scores on the extremes of any given distribution, it thus emerges as the measure of choice in variability. Assignment 2 Sales 500 salespeople of a company are mostly normally distributed forming a bell symmetrical shape. Whereby sales from those who record high sales appear on the right side while those with low sales coming on the left side and with a majority of sales appearing on the middle part of the distribution, translating to an average of sales on either side of the curve accounting for the mean sales. This would make it resourceful to come up with a working model to be used to work out a budget as well as predicting performance of the company. A company would predict the effect-increase in sales revenue- of increasing the number stores and salespeople. This distribution also helps to not only identify those sales people who need extra training but also it helps to identify those who need to be replaced. It is worth to consider the size of the sample in question, with a large sample like that of the 500 sales people proving to be more representative compared to a sample of about 100 people. It is therefore relevant statistically to estimate that adding one more sales person is worth for instance $25,000 increase in revenue. Clearly from the study sales people and their respective sales are the main variables which are measured in ratio scale since there are those sales people who have nil sales. On using a continuous scale, sales are normally distributed with most of sales in middle range and the entire sales data being within the range 40% of the average sale. A probability value of 0.05 implies 5% of the sales people will sell an amount different from expected sales value and while the remaining 95 % are expected to sell at an amount within the expected amount. This concept is therefore used to represent monthly countable sales. Assignment 3 Organizations resort to using means such as incentives and bonuses so as to increase the productivity of their employees. In order prove that financial incentives have always boosted the productivity of employees, I will evaluate the hypothesis that a $ 1,000 incentive offered to employees is sufficient to make them finish a project before the expected time. In this study size of incentive and level of productivity are the independent and dependent variables respectively. Assuming the population sample n=30 would be chosen randomly from the employees allocated to new projects. Hypothesis testing is an analysis of a given research, with a null hypothesis indicating a zero change as a result of the $ 1000 incentive represented by µ. On the other hand a change as a result of the $ 1000 incentive indicates the alternative hypothesis. In order to determine critical boundaries and identify chances of Type 1error, it's important to select an alpha level. Selecting a .01 alpha level provides a low risk error and avoids overstretching the critical area since this level enhances a balance between the functions which offers a base to reject or accept the proposed effect of the incentive. A one-tailed test is utilized when hypothesis about a particular directional rather than general. Results obtained from one -tailed test are of significance ...Download file to see next pagesRead More
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