Lead time for a given item is 3 weeks and sales have been recorded in 1 week intervals. If the Standard Deviation for the sales interval is 25 then the Standard Deviation for the lead time should be approximately:
A) 25
B) 43
C) 75
D) 14
E) 8

Question

Quizplus · Accepted Answer

The lead time is the duration between placing an order and receiving the item. If sales have been recorded in 1 week intervals, then we can assume that orders are placed at the start of each week. Since the lead time is 3 weeks, this means that the item is received at the start of the fourth week. Therefore, the lead time is equal to the sum of three 1-week intervals.

If the Standard Deviation for the sales interval is 25, then we can assume that the Standard Deviation for each 1-week interval is also 25. This means that the variance for each 1-week interval is 25 squared or 625.

For the lead time, we know that the variances add up, so the variance for the lead time is equal to 3 times the variance for a 1-week interval, which is 3 times 625 or 1875.

Therefore, the Standard Deviation for the lead time is the square root of the variance, which is the square root of 1875 or approximately 43 (rounded to the nearest whole number).

So, the answer is B) 43.

Lead Time for a Given Item Is 3 Weeks and Sales