The injection modeling department of a company used 40 pounds of a powder a day. Inventory is reordered when the amount on hand is 240 pounds. Lead time averages five days. It is normally distributed and standard deviation of 2 days. What is the probability of a stockout during lead time?

the probability of stockout is 63.06%

Explanation:

since the time for stockout is 240 pounds / 40 pounds/day = 6 days if there is no replenishment, then for a lead time of 6 days or more, there is stockout. If the random variable X = lead time, distributes normally then the probability of a stockout Ps will be:

Ps = P (X≥6 days)

for the normalised random variable Z

Z = (X-μ) / σ, where μ = expected value of X, σ = standard deviation of X

then

P (X≥6 days) = P (Z≥ (6 days-5 days) / (2 days)) = P (Z≥ 0.5)

from normal distribution tables

P (Z≥ 0.5) = 0.6306 = 63.06%