Mopeds (small motorcycles) are very popular in Europe because of their mobility, ease of operation, and low cost. Assume a normal distribution of the speed with mean value 46.8 km/h and variance 3.24 km/h.a) What is the probability that maximum speed of a moped is at least 48 km/h?[10 points]b) What is the probability that maximum speed of a moped is between 44.5 km/h and 48.5?[10 points]c) What proportion of the maximum speed of a moped will be either smaller than 42.9 km/h or higher than 47.2 km/h?[10 points]d) What is the probability that maximum speed of a moped differs from the mean value by at most 1.5 standard deviations?