Question

A wholessale disstribution of a tablet compresion machine finds that the annual demand for the product is normal distribution with mean 140 and standared deviation of 15. ifhe orders only once in a year. What quantity should be ordered to ensure that there is only 5% chance of running short

Answer 1

Let $X=$ the number of units of product: $X\sim N(\mu, \sigma^2)$

Given $\mu=140, \sigma=15.$

$$P(X>x)=1-P(X\leq x)=$$

$$=1-P(Z\leq \dfrac{x-140}{15})=0.05$$

$$\dfrac{x-140}{15}=1.645$$

$$x=165$$

165 units should be ordered to ensure that there is only 5% chance of running short.