The normal distribution with the mean and standard deviation of the lead time demand can be used to calculate the likelihood that an item will be in stock during the delivery lead time. We must first determine the lead time demand. Given that the delivery lead time is 4 days and the average daily demand is 100 cases, the lead time demand is as follows: Lead time demand = average daily demand x lead time = 100 x 4 = 400 cases The standard deviation of the lead time demand, which is equal to the square root of the sum of variances, must then be determined: Lead time demand standard deviation = sqrt(lead time x variance) = sqrt(4 x (20)^2) = 40 Now we can calculate the z-score, which is the number of standard deviations the lead time demand is from the mean demand: z-score = (re-order point - lead time demand) / lead time demand standard deviation = (442 - 400) / 40 = 1.05