1. (lpts) Suppose the following table gives the maximum wind speed and category probabilities of a hurricane for 24 hours from now Wind Speed 39 73 74 95 96 110 111 13B 131 155 > 155 Category 0 1 2 3 4 5 Probability 12% 20% 50% 14% 3% 1% (a) Using the \"Category\" as Xi, nd the mean and standard deviation of this probability distribu- tion. (b) Using the midpoint of Wind speed as X,- (and 165 for the midpoint of category 5), nd the mean and standard deviation of this probability distribution. (c) Graph the probability distribution for the discrete random variable \"Predicted Hurricane Cat- egory\" (as given above) in the graph below