 1.7. This shows the probability that The standardised normal curve now becomes as in Equation 1.40. 1/8 Statistical analysis (1.40) Table 1.1 Area under the normal curve from to w The total area under the standardised normal curve is unity and the area between any two values of w is the probability of an item from 0.500 0.508 0.516 0.524 0.532 the distribution falling between these values. The normal curve 0.540 0.548 0.556 0.564 0.571 extends infinitely in either direction but 68.26% of its values (area) fall between + o, 95.46% between I 2o, 99.73% between I 30 and 0.579 0.587 0.595 0.603 0.610 99.994% between I 4o. 0.618 0.626 0.633 0.640 0.648 Table 1.1 gives the area under the normal curve for different values of W. Since the normal curve is symmetrical, the area from 0.655 0.663 0.670 0.677 0.684 w to + 8 is the same asfrom-wto-.As - an example of the use 0.692 0.700 0.705 0.712 0.719 of this table, suppose that 5000 telephones have been installed in a 0.726 0.732 0.739 0.745 0.752 city and that they have a mean life of 1000 weeks with a standard deviation of 100 weeks. How many telephones will fail in the first 0.758 0.764 0.770 0.776 0.782 800 weeks? From Equation 1.39, expression 1.41 is obtained. 0.788 0.794 0.800 0.805 0.811 (1.41) 0.816 0.821 0.826 0.832 0.837 0.841 0.846 0.851 0.855 0.860 0.864 0.869 0.873 0.877 0.881 Ignoring the negative sign, Table 1.1 gives the probability of telephones not failing as 0.977 SO that the probability of failure is 1 0.885 0.889 0.893 0.896 0.900 0.977 or 0.023. Therefore 5000 X 0.023 or 115 telephones are 0.903 0.907 0.910 0.913 0.916 expected to fail after 800 weeks. 0.919 0.922 0.925 0.928 0.931 1.9.4 Exponential distribution 0.933 0.936 0.938 0.941 0.943 0.945 0.947 0.950 0.952 0.954 The exponential probability distribution is a continuous distribution and is shown in Figure 1.9. It has the form given in Equation 1.42, 0.955 0.957 0.959 0.961 0.963 where x is the mean of the distribution. 0.964 0.966 0.967 0.969 0.970 (1.42) 0.971 0.973 0.974 0.975 0.976 0.977 0