The Central limit theorem is a very powerful tool in statistical inference and Mathematics in general, since it has numerous applications such as in topology and many other areas. For the case of probability theory, it states that, “given certain conditions, the sample mean of a sufficiently large number or iterates of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normally distributed”. In the research paper, three different statements of our theorem (CLT) are given. This research paper has data regarding the shoe size and the gender of the of the university students. The paper is aimed at finding if the shoe sizes converges to a normal distribution as well as find the modal shoe size of university students and to apply the results of the central limit theorem to test the hypothesis if most university students put on shoe size seven. The Shoe sizes are typically treated as discretely distributed random variables, allowing the calculation of mean value and the standard deviation of the shoe sizes. The sample data which is used in this research paper belonged to different areas of Kibabii University which was divided into five strata. From two strata, a sample size of 74 respondents was drawn and from the remaining three strata, a sample of 73 students per stratum was drawn at random which totaled to a sample size of 367 respondents. By analyzing the data, using SPSS and Microsoft Excel, it was vivid that the shoe sizes are normally distributed with a well-defined mean and standard deviation. We also proved that most university students put on shoe size seven by testing our hypothesis using the p-value. The modal shoe size for university students was found to be seven since it had the highest frequency (97/367). This research was aimed at enlightening shoe investors, whose main market is the university students, on the shoe sizes that are on high demand among university students.

This paper is based on electricity consumption pattern in rental houses around Kibabii University (KU) situated in Western region of Kenya. Because of unexpected blackout faced by nonresident students at the time they need electricity most for their studies, this work intends to find out the directive measure to curb this crisis. Since the usage of electricity showed high relationship to the number of households sharing a common meter, Regression analysis prove to be the most effective method to model a solution to this problem. SPSS was used to analyze the data obtained. The results showed the consistency in linear trend of usage of electrical power on a monthly basis among students, it is observed also that the rate of consumption of power among nonresident students of KU is affected by the number of households sharing the meter. The consequence of this study is that with the correct data in place one is able to know the amount of power in kilowatt-hours needed for consumption throughout the semester and plan effectively so that power loss is not experienced. The results will be so useful to the KPLC (Kenya Power and Lighting Company) and KU fraternity for planning purposes.