Lead time is exactly 20 days long.Daily demand is normally distributed with a mean of 10 gallons per day and a standard deviation of 2 gallons.What is the standard deviation of demand during lead time?
A)20 x 2
B)20 x 10
C)2 times the square root of 20
D)2 times the square root of 10
E)none of the above

Question

Quizplus · Accepted Answer

The standard deviation of demand during lead time can be calculated as the square root of the sum of the variances of daily demand over the lead time. The variance of daily demand is the square of the standard deviation, which is 2^2 = 4. Since there are 20 days in the lead time, the variance of demand during lead time is 20 x 4 = 80. Therefore, the standard deviation of demand during lead time is 2 times the square root of 80, which simplifies to 2 times the square root of 16 times 5, or 2 times 4 times the square root of 5, which is approximately 8.94. So the closest choice to this is C.

Lead Time Is Exactly 20 Days Long