2. Suppose that at a gas station the daily demand for regular gasoline is normally distributed with a mean of 1000 gallons and a standard deviation of 100 gallons. The station manager has just opened...

2. Suppose that at a gas station the daily demand for regular gasoline is normally distributed with a mean of 1000 gallons and a standard deviation of 100 gallons. The station manager has just opened the station for business and there is exactly 2300 gallons of regular gasoline in storage. The next delivery is scheduled later tomorrow at the close of business. (a) Let X1 and X2 denote the demand of today and tomorrow, respectively. Let X = X1 + X2. Find the distribution of X. (b) Find the probability that the manager will have enough regular gasoline to satisfy today’s and tomorrow’s demand.