Elastic optical networks enhance the flexibility of bandwidth distribution and making it precise, enables optimal use of the spectrum. The routing and spectrum problem (RSA) in spectrum-sliced elastic optical networks is addressed by a unique technique of spectrum allocation that uses Gaussian distributions. The routing algorithms used include balanced load spectrum allocation and shortest path spectrum reuse. The results show that using a Gaussian distribution method to distribute spectrum provides less blocking probability. For a 6-node and 14-node NSFNET topology networks with static traffic demands, the blocking probability of the algorithm is studied. The blocking probability for the proposed distributions is obtained and compared with the gold-fit algorithm and first-fit, exact-fit algorithms. The proposed algorithm shows the least blocking probability of 0.0125 for 150 cumulative average demand when compared to other algorithms.