Question

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?

Answer 1

the probability of stockout is 63.06%

Step-by-step 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%