Higher Concepts of Mathematics STATISTICSSolution:The mean is[40(4)+38(3)+36+34(2)+30+28(3)]/14= 492/14 = 35.1The mean variance is:1144035.13835.12835.1... 3635.1114(57.8)4.12From the tank mean of 35.1%, it can be seen that a 40% increase in level will statistically fit intothe tank; 35.1 + 40 <100%. But, the mean doesn’t tell us if the level varies significantly overtime. Knowing the mean variance is 4.12% provides the additional information. Knowing themean variance also allows us to infer that the level at any given time (most likely) will not begreater than 35.1 + 4.12 = 39.1%; and 39.1 + 40 is still less than 100%. Therefore, it is a goodassumption that, in the near future, a 40% level increase will be accepted by the tank without anyspillage.NormalDistributionThe concept of a normal distribution curve is used frequently in statistics. In essence, a normaldistribution curve results when a large number of random variables are observed in nature, andtheir values are plotted. While this "distribution" of values may take a variety of shapes, it isinteresting to note that a very large number of occurrences observed in nature possess afrequency distribution which is approximately bell-shaped, or in the form of a normaldistribution, as indicated in Figure 1.Figure 1 Graph of a Normal Probability DistributionRev. 0 Page 7 MA-05