STATISTICS Higher Concepts of MathematicsThe significance of a normal distribution existing in a series of measurements is two fold. First,it explains why such measurements tend to possess a normal distribution; and second, it providesa valid basis for statistical inference. Many estimators and decision makers that are used to makeinferences about large numbers of data, are really sums or averages of those measurements.When these measurements are taken, especially if a large number of them exist, confidence canbe gained in the values, if these values form a bell-shaped curve when plotted on a distributionbasis.ProbabilityIf E_{1}is the number of heads, and E_{2}is the number of tails, E_{1}/(E_{1}+ E_{2}) is an experimentaldetermination of the probability of heads resulting when a coin is flipped.P(E_{l}) = n/NBy definition, the probability of an event must be greater than or equal to 0, and less than orequal to l. In addition, the sum of the probabilities of all outcomes over the entire "event" mustadd to equal l. For example, the probability of heads in a flip of a coin is 50%, the probabilityof tails is 50%. If we assume these are the only two possible outcomes, 50% + 50%, the twooutcomes, equals 100%, or 1.The concept of probability is used in statistics when considering the reliability of the data or themeasuring device, or in the correctness of a decision. To have confidence in the values measuredor decisions made, one must have an assurance that the probability is high of the measurementbeing true, or the decision being correct.To calculate the probability of an event, the number of successes (s), and failures (f), must bedetermined. Once this is determined, the probability of the success can be calculated by:pssfwheres + f = n = number of tries.Example:Using a die, what is the probability of rolling a three on the first try?MA-05 Page 8 Rev. 0