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?

Option A

$20$ times $2$

Option B

$2$ times the square root of $10$

Option C

$400$ times the square root of $10$

Option D

$20$ times $10$

Option E

$2$ times the square root of $20$