The lottery results encapsulated in Fig. 3.9 are based on six numbers being selected from the integers 1, 2, 49·The distribution of these numbers should follow the functional form given in Exercise (3.2). Use the results of that exercise to predict the mean and stan- dard deviation expected for this distribution. How do these compare with the results for the year 2000, with a mean of 25.4, and standard deviation 14.3? The lottery has six numbers selected, with the mean readily calcu lated. Based on the central limit theorem we expect the distribution of the means to follow a Gaussian distribu- tion with a standard deviation which is v6 smaller than the original distribution. What do you predict for the mean and standard deviation of the means? How do these compare with the results for the year 2000, with a mean of 25.4, and standard deviation 5.7?