Question

Daily usage is exactly 60 gallons per day. lead time is normally distributed with a mean of 10 days and a standard deviation of 2 days. what is the standard deviation of demand during lead time? 60 times 10 60 times the square root of 10 60 times the square root of 2 10 times the square root of 2 60 times 2

Answer 1

The standard deviation of demand during lead time can be calculated as the daily usage multiplied by the square root of the lead time. In this case, the standard deviation is approximately 189.74 gallons.

Step-by-step explanation:

To find the standard deviation of demand during lead time, we need to use the formula:

Standard deviation of demand during lead time = daily usage * square root of lead time

Given that the daily usage is 60 gallons per day and the lead time has a mean of 10 days and a standard deviation of 2 days, we can substitute these values into the formula:

Standard deviation of demand during lead time = 60 * square root(10) = 60 * 3.1623 ≈ 189.74

Therefore, the standard deviation of demand during lead time is approximately 189.74 gallons.

Answer 2

We are told that the daily usage is exactly 60 gallons per day, therefore the total number of gallons that is used during the mean lead time is also called the mean demand amount:

Mean demand amount = Daily usage * Mean lead time

Mean demand amount = (60 gallons / day) * 10 days

Mean demand amount = 600 gallons

Since the standard deviation of the lead time is 2 days, therefore the standard deviation of the demand should also be:

Standard deviation of demand = Daily usage * Standard deviation of lead time

Standard deviation of demand = (60 gallons / day) * 2 days

Standard deviation of demand = 120 gallons

Short answer:

60 times 2