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.

The purpose of this paper is to determine the time that a patient can spend waiting for service in Kibabii University Healthcare Clinic in Bungoma County (Kenya). The main objective was to provide necessary information to service facility managers, stakeholders, hospital staffs and other related institutions with the knowledge to improve the queuing system or to curb long waiting time of patients seeking services which can cause deterioration of the disease and sudden demise. This project also aims at providing suggestions to various factors identified to be the causes of long waiting time in the outpatient department at Kibabii University healthcare to help the smooth running of the clinic. The ODK tool was used in data collection procedure to capture the opinions of the respondents. The results from the ODK Tool was exported to XLS which is an export feature of data to excel, later data was exported to SPSS for analysis from excel.

This paper is aimed at presenting the temporal and spatial variability of rainfall over Bungoma region between 2000 and 2015. Rainfall data was obtained for 5 stations in the region. The data was subjected to analyses by use of Microsoft Excel and SPSS. The results from analysis of the data showed that the March, April, and May (MAM) and October, November, and December (OND) rainfall totals showed a general increasing trend in all the stations. The MAM season was found to have the most reliable rainfall in all stations while the OND season was reliable in some of the stations in the study region. Kanduyi region is seen to receive the highest amount of rainfall all through the years, and Tongaren the Least amount of Rainfall. The significance of these findings is that it could be used by various policymakers and development partners for planning purposes.