Statistics for Decision Making / QNT/275
University of Phoenix
Statistics in Business
Statistics is the method in which you analyze collected data. For statistics to be effective, you must collect good data and then analyze it correctly. If you do not collect good data, then there is no need to analyze it. If you collect good data and do not analyze it correctly, then you are not taking full advantage of this powerful tool called statistics. Statistics are in all professions and is an excellent tool to keep businesses running efficiently and effectively.
The normal distribution is the most important pattern of data that occurs in statistics. Rongrong Xie writes in The American Statistician that the reason the normal distribution is interesting is that it has an important use in the statistical theory of drawing conclusions from sample data about the populations from which the samples are drawn.
A practical example: Suppose you must establish regulations concerning the maximum number of people who can occupy an elevator. You know that the total weight of eight people chosen at random follows a normal distribution, with a mean of 1210 pounds and a standard deviation of 330 pounds. What is the probability that the total weight of eight people exceeds 1320 pounds?
The mean is 1210, and we are interested in the area that is greater than 1320. z = (x - m) / s
Here x = 1320 m, the mean = 1210 s, the standard deviation = 330
Z is how many standard deviations from the mean the value, x that was provided in this example: z = ( 1320 - 1210 ) / 330 z = 110 / 330 z = 0.33
In other words, the value x is one-third of a standard deviation away from the mean.
Look in the normal distribution table down the left-hand column for z = 0.3, and across under 0.03. The number in the table is the tail area for z = 0.33 which is 0.3707. This means that 37% of the time, due to chance, the weight of the eight people chosen at random would exceed 1320. This would be relevant to the design of an elevator. If the failure weight on the elevator mechanism was 1320, then 37% of the time there would be a catastrophic failure. Consequently, in designing elevators, manufacturers would probably opt to design five for six standard deviations. This is the probability that the weight will exceed 1320 pounds. The answer is that the probability that the total weight of eight people exceeds 1320 pounds is 0.37 or 37%.
If you have the mean of a sample, you can use the normal distribution tables to find out probabilities. The distribution of an average tends to be normal, even when the distribution from which the average is computed is not normal. Sample means have normal distribution no matter how abnormal the distribution of the original population was. Jeffrey Blume explains in The American Statistician that people can then easily visualize the theorem when they understand that as the sample size increases, the distribution of the sample average approaches the bell-shaped curve.
A different example of how statistics is applied in business is using