Mean Temperatures for Boston in the Month of July
Normal Distribution
The results from the graph above indicate a normal distribution. A normal distribution curve is characterized by a bell-shaped curve, which is symmetrical around the average (Daskalakis, Diakonikolas, & Servedio, 2015). A normal distribution curve has the same median, mode, and mean, which is exhibited in the above graph as the average splits the area into halves.
Outliers
An outlier can be described as a point that is lying outside the pattern of a general distribution curve. In the above graph, there are no outliers as the points are placed at a small distance away from each other (Daskalakis, Diakonikolas, & Servedio, 2015). There is not a single point that has any significant difference from the other points in the observation.
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Mean of 76
The probability that in any month of July, the mean temperature will be over 76 can be computed using the normal distribution function in excel. First, the standard deviation is computed, and the value obtained is 4.344082484 (Gnedenko, 2018). Using the standard deviation, the calculated probability for the mean temperature for the month of July less than 76 is 0.24491. Thus, to obtain the probability of the mean that will be beyond 76 for the same month will be 1 – 0.24491 = 0.75509, same as 75.51%.
Mean of over 80 for any July
To get the probability of any month of July having a mean temperature above 80, the same excel function was employed. Using the normal distribution function, the same standard deviation value of 4.344082484 was used (Gnedenko, 2018). The obtained mean for the month of July less than 80 was found to be 0.05354765. Therefore, the mean for temperature above 80 will be 1 – 0.05354765 = 0.94645235, which is the same as 94.65%.
Heatwave
The probability that there would be a heatwave in the next ten days is 0.94645235-0.75509=0.19136235 an equivalent of 19.14%.
Customer Surveys
Binomial Distribution
The situation fits a binomial distribution because, in each of the trials in the customer survey, there are only two results: the customers buying the products online or purchasing from a physical store. Furthermore, the probability of the results from any of the trials remains constant throughout time (Gnedenko, 2018). Additionally, the trials are independent, statistically meaning that the results of any of the trials cannot interfere with the results of the other trial.
Probability of Twelve Sales Exactly Four Online
From the computation on excel, the probability of twelve sales, exactly four being online is 0.999198899.
Probability of Twelve Sales Less Than Six Online
The probabilities of twelve sales being less than six online were also calculated by excel, and the value found to be 0.991024545.
Probability of Twelve Sales More Than Eight Online
To obtain the probability of twelve sales more than eight online, binomial distribution was used in excel to obtain a probability of 0.94268879.
Huawei’s Use of Probability and Distributions
The company is facing a ban from manufacturing and selling its handsets within the American market. The company could benefit from using probability and distributions to determine the market share they stand to lose following the ban. As a research analyst for the company, I would collect data on the number of mobile handsets sold through online and those sold on physical stores to create a binomial distribution (Gnedenko, 2018). Questions that would be asked include:
What is the chance that the company will sell fewer than 20% of its handsets through physical stores?
What is the chance that over 50% of the handsets will be sold online?
What is the chance that over 80% of the handsets will be sold online?
By calculating the probabilities, the company will learn whether it is feasible to maintain its market share through online sales. The data is crucial for the company as America forms one of the largest markets for the company (Gnedenko, 2018). Moreover, there are manufacturing plants that the company has established within the country. Thus, the ban will mean decreased production as well as income for the mammoth telecommunication company. It is critical that the company collect the data as it will assist in the increasing of the income through reaching the American market through alternative means.
References
Daskalakis, C., Diakonikolas, I., & Servedio, R. A. (2015). Learning poisson binomial distributions. Algorithmica, 72(1), 316-357.
Gnedenko, B. V. (2018). Theory of probability. New York; Routledge.
