Answer to Question #344882 in Statistics and Probability for Akshay

Question

Universal autos sell a popular motor oil. They place a replenishment order when the stick of this oil drops to 20 gallons. The store manager is concerned that the sales are being lost due to stockouts while waiting for an order. It has been determined that the demand during replenishment lead-time is normally distributed with a mean of 15 gallons and a standard deviation of 6 gallons. The manager would like to know the probability of a stockout.

Answer 1

$$P(X<20)=P(Z<\dfrac{20-15}{6})$$

$$\approx P(Z<0.8333)\approx0.7977$$